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ANCIENT INDIAN CHRONOLOGY 

ILLUSTRATING 

SOME OF THE MOST IMPORTANT 
ASTRONOMICAL METHODS 



BY 
PRABODH CHANDRA SENGUPTA, M.A., 

LATE PROFESSOR OF MATHEMATICS, BETHUNE COLLEGE, CALCUTTA, ' 
SOMETIME LECTURER IN INDIAN ASTRONOMY AND MATHEMATICS 
AT THE CALCUTTA UNIVERSITY 




UNIVERSITY OF CALCUTTA 
1947 

Rs. 




IN INDIA 



FEINTED AND PUBLISHED BY NISHITOHANDKA SKN, 
UPBBINTENDENT (OTTO.), CALCUTTA UNIVBRSITY PBBS1, 
48, HA2EA ROAD, BALL^GUNQS, CALCUTTA. 



U08B November, 



CONTENTS 

PREFACE ... ... ... y 

INTRODUCTION ... vii 

SPECIAL NOTE TO CHAPTER VI xxvii 

Section Chapter Name of Chapter Page 

I Date of the Bharata- Date of the Bharata-Baitle, 

Battle ... I Mahabharata Evidences ... 1 

II Bharata Battle Tradition (A) 34 

III Do. (C) 46 

II Vedic Antiquity IV 7 Madhu-Vidya or Science of 

Spring 60 

,, V When Indra became Maghavan 72 

,, VI Ilbhus and their awakening by 

the Dog 82 

,, VII Tradition of Indra's Victory 

over Asuras ... 90 

,, VIII Miscellaneous Indications of 

Vedic antiquity ... 95 

, f IX The Solar Eclipse in the 

!Rgveda and the Date of Atri 101 

X Heliacal Eising of 

X and v Scorpionis ... 132 

XI Yama and his Two Dogs ... 137 

, , XII Legend of Prajapati and Echini 147 

f , XIII Solstice Days in Vedic Litera- 

ture and the Date of Yajur- 



IV 



ANCIENT INDIAN CHEONOLOGY 



Section Chapter 

III Brahmana XIV 
Chronology 

XV 



XVI 

XVII 

XVIII 

XIX 



99 
99 



XX 



IV Indian Eras XXI 



XXII 
XXIII 



V 



ERRATA 



XXIV 
XXV 

XXVI 



Name of Chapter 

Solar Eclipse' in tbe Tandya 
Brabmana ... 

Time Reference from the 
Jaimimy a Brahmana . . . 

Vedanga and Maitrl Traditions 
Sariikhayana Brahmana 
Baudhayana Srauta Sutra 
Satapatha and Tandya 

Brahmanas ...... 

Katyayana and Apastamba 
Srauta Sutras ...... 

Eclipses in the Samyukta 
Nikaya and the Date of the 
Buddha's Nirvana ... 

Kani ska's Era ...... 

Earlier Era of the Kharothl 

Inscriptions ... , , 

Samvat or the Malava Era ,,. 

The Gupta Era ...... 

Date of Kalidasa ...... 

Epilogue ...... 



Page 

175 

183 
189 
19 i 
198 

208 
212 



217 
222 

229 
235 



263 
279 



PREFACE 

I published in the Journal of the Royal Asiatic Society 
of Bengal, Letters, in the years 1988 and 1939, the 
following five papers : 

(i) Some Astronomical References from the Maha- 
bharata and their Significance in Vol II , No. 10. 

(it) Bharata-Baltle Traditions. ^ Published 

(Hi) Solstice Days in Vedic Literature. f in 

(iv) Madhu-vidyaor the Science of Spring. C Vol. IV, 
(v) When Indra became Maghavan. ) Nos. 15-18 

The last four of the above papers were kindly communi- 
cated to the Royal Asiatic Society of Bengal by Prof. 
M. N. Saha, F.R.S., who had found in these papers methods 
and results in Ancient Indian Chronology which deserved 
encouragement. It was at his suggestion that I submitted 
to the authorities of the Calcutta University, in a letter 
dated the 23rd August, 1939, a scheme for publication of a 
research work on Indian Chronology, The University very 
kindly sanctioned my scheme in their Minutes of the Syndi- 
cate, dated the 30th September, 1939, and appointed Mr. 
Nirmalchandra Lahiri, M.A., to assist me in my research 
work. Under the very favourable conditions thus created 
by the University i took up work under the scheme from 
Nov., 1939, which was finished by July, 1941 in the form 
of the present work Darned ''Ancient Indian Chronology." 

The five papers mentioned above formed the nucleus of 
the present work. The last four of the above-named papers 
were noticed in the famous British Science Journal, 
"Nature" in Vol. 145, Jan., G, 1940, in the Section of 
"Research Items/' under the caption, "Some Indian 
Origins on the light of Astronomical Evidence" which is 
quoted at the end of this work. 

I have carried on the researches embodied in the present 
work in the spirit of a sincere truth seeker. If I have been 
led by any bias my critics will kindly correct me and point 



vi ANCIENT INDIAN CEBONOLOGY 

out the same to me. I have not hesitated to reject some 
of my former findings when further study and new light 
received therefrom justified such action. I trust my work 
will be continued by other Indian researchers in the same 
line in future. 

I have to acknowledge my indebtedness to the works 
of the late Prof. JacobP, Tilak 2 and Dlksita 3 on Vedic 
Chronology. To the works of Tilak and Dlksita I am 
indebted for many references from the Vedas, but in many 
cases my interpretation has been different from theirs. 

I have also to acknowledge with thanks the sympathy 
and help with which I was received by Mm. Vidhusekhara 
Sastrl, late Asutosh Professor of Sanskrit, Calcutta Univer- 
sity and his colleague Mm. Sltarama Sastri, whenever I 
approached them as to the correct interpretation of Vedic 
passages. To Prof. Dr. M. N. Saha, F.E.S., I am indebted 
for constant encouragement and help in the matter of 
making many books accessible to me and for many helpful 
discusssions and criticisms. I have to express iny thanks to 
the authorities of the Calcutta University, and specially to 
Dr. Syamaprasad Mookerjee, M.A., B.L., D.Litt., Bar.-at- 
LaWj M.L.A., late President of the Council of Post- 
Graduate Teaching in Arts, for creating this facility for me 
to carry on my researches, 

Finally I have to, pay my tribute of respect to the 
memory of the late Sir Asutosh Mookerjee, the inspirer 
and organiser of research studies at the Calcutta University, 
and of the late Maharaja Sir Manindrac handra Naadi, 
K.C.I.E., of Cossiinbazar, the donor of the fund created 
for Research work in Indian Astronomy, from which was ' 
met the major expenses in carrying out the researches. 

Calcutta, October t 1947. P. C. SENGUPTA, 

1 "On the Date of the Bgveda' 1 Indian Antiquary, Vol, xxiii, pp. 154-159. 



INTRODUCTION 

The word * chronology ' meant apparent dating only, 
from" the 16th century of the Christian era. The word has 
now come to mean * the science of" computing and 
adjusting time and periods of time, and also of recording 
and arranging events in order of time ; it means com- 
putation of time and assignation of events to their correct 
dates." * In the present work, it is the science of 
Astronomy alone that has been brought into requisition in 
ascertaining the dates of past history of the Hindus, both 
of the Vedic and of later times. The data for dates 
arrived at from 4170 B.C. to 625 B.C. have been 
derived from the sources which are either of the Vedic or 
post- Vedic Sanskrit literature. In the section on the 
Indian eras* they have been derived chiefly from the 
archaeological sources. 

Now, chronology is based on the interpretation that we 
may put to any statement which is derived either from the 
literary or epigraphic sources. Whether the interpreta- 
tions accepted in the present work are justifiable, is a 
point that is to be decided by the author's critics. So far 
as he IB concerned be has this satisfaction that he could 
not find any better interpretations than what, he has 
accepted of the astronomical references which he could- 
discover and use for the present work. It is made op-bf 
the following sections, viz., the Date of Bharata Battle, 
the Vedic Antiquity, BrShnaana -Chronology, and on the 
Indian Kras. It has not been possible to ascertain any 
dates from any other Srauta Sutras excepting those of 



viii ANCIENT INDIAN CHRONOLOGY 

Baudhayana, Katyayana and Apastamba. The Grhya 
Sutras do not present any new indication of dates. 

The results of the findings may be briefly stated thus : 
The date of the Bharata Battle has been proved to have 
been the year 2449 B.C., so far as evidences can be 
discovered from the 'Sanskrit literature, no other date for 
the event is now possible. The antiquity of the Bgveda as 
shown in the chapters af the book extend from 4000 B.C. 
to perhaps 2450 B.C. The Atharva Veda indications also 
point to dates from 4000 B.C. to about 2350 B.C., viz., 
the time of Janamejaya Pariksita, while the different 
sections of the Yajur-veda show a range of dates beginning 
from about 2450 B.C. 

As to the Brahmanas and Sraida tfutras, they are books 
on rituals only and as such they cannot belong to the 
same antiquity as the Vedas themselves, more specially the 
Rg-veda. The range of dates obtained for this type of 
works extends from about 1625 B.C. to about 630 B.C. So 
far as my studies go, the Yajurveda itself is more or less a 
Brdhmana or a work on rituals. The Brahmanas as a 
rule record the traditional days for beginning the sacrifices 
which indicate the earliest date of about 3550 B.C. Such 
statements, however, cannot give us the dates of the 
Brahmanas which record them. 

The Srauta Sutras generally are crude followers of 
earlier rules as to the beginning of the year, the same 
remarks are applicable to all the Grkya Sutras. The 
Jyautisa Vedangas indicate a date of about 1400 B.C. Iru 
the section of the Indian Eras, it has been shown that the 
Buddha's Nirvana era should be dated at 644 B.C., if the 
eclipses spoken of in the Samyukta Nikaya can be held as 
real events happening in the Buddha's life time. It has 
also been shown that the zero year of the early Kharosthi 
inscriptions, should be taken as the year 305 B.C., the era 
itself may be called that of Selukus Nikator ; the zero year 



INTBODUCTION ix 

of the later KharosthI inscriptions or of Kaniska's era was 
80 A.D. ; while of the current Sakaerathe Zero year is 77-78 
A.D. It has been shown in the chapter on the Samvat or 
Malava era, that it was started from 57 B.C. which is 
reckoned as the year 1 of this era. An attempt has been 
made to show why the years of this era are called Krta 
years. The Zero year of the Gupta era should definitely 
be taken as the year 319 A.D. or 319-20 A.D, ; or the 
Saka year 241 as recorded by Alberunl. The date of 
Kalidasa has been ascertained as the middle of the sixth 
century of the Christian era. The modern Ramayana may 
be dated about a hundred years earlier than the time of 
Ivalidasa. 

One point-that I specially want to emphasise is this : 
The date of a book may be much later than the date of an 
event which it records. The Rama story is certainly much 
older than the time of the Pandavas, but the modern work 
R&mayana cannot be dated earlier than about 450 A.D. 
The date of the Bhftrata Battle is 2149 B.C., but the book, 
the present Mah&bh&rata must be dated about 400-300 B.C. 
The Vedic antiquity runs up to 4000 B.C., but the date 
when the Tlgveda was written in the form in which we get 
it now, must be dated much later. To ascertain this later 
date is perhaps not possible. The points to be settled are 
(L) When did the present highly scientific Indian alphabet 
come into being? ( W 2) What alphabet was in use amongst the 
Hindus for recording their Vedic songs and other literature? 
(8) What were the earliest vocal forms of the words used 
in the Vedas? We therefore conclude that the antiquity 
of the Vedic culture is one thing while the date of the 
present Rgvedu in another, the date of the Bharata Battle 
is one thing while the date of the modern Mahabharata is 
another, the date of Kama or the Rama story is one thing 
while the date of the modern Ramayana, is another. The 



xii ANCIENT INDIAN CHRONOLOGY 

suktas or hymns in the 3rig-Veda, M. X, 30-34. All these 
considerations lead us to conclude that the latest portions of 
the Rg-Veda were composed at the time of the Pandavas 
(2449 B.C.), when according to tradition the Vedas were 
subdivided into $fe, Sama ahd Yajus, and the author of 
thip division was Vyasa the common ancestor of the 
Kauravas and the Pandavas. The Alharva Veda, in my 
opinion, records traditions which are as old as of the !Rg- 
Veda itself, as may be seen from Chapters VIII, X and XL 
As this Veda (Atharva) says 1 *ra?f *raro l or "that 
the (southerly) course is at the Maghas in my time*' 
and an: U *B$wf?T ^ THJ: qrftftRfl s or " that man 
prospers well in the kingdom of Pariksiin," I understand 
that the time indicated is between >J14{) to 2350 B.C. Thus 
according to 'the evidences cited above, the Atharva Veda 
also was completed about the time of the Pandavas. 

Vedic Antiquity and the Indux Valley civilisation 

In the Eg- Veda we get the following references to the 
fSi&nadevasi: 

(a) M. VII, 21, 5 : 

*r snr 



'* Let not the Baksasas, Indra, do us harm: let not 
the evil spirits do harm to our progeny, most powerful 
Indra ; let the sovereign lord (Indra), exert himself (in the 
restraint of) disorderly beings, so that the unchaste 
devas) may not disturb our rite/' (Wilson) 

(6) M. X, 99, 3 : 



INTRODUCTION xiii 



f * Going to the battle, marching with easy gait, desiring 
the spoil, he set himself to the acquisition of 'all wealth. 
Invincible, destroying the Phallus-worshippers ( 



he won by his prowess whatever wealth (was concealed) 
in the city with hundred gates." (Wilson) 

It appears that these Phallic- worshippers were a rich 
people living in large cities, which were raided by the 
worshippers of Indra and other Vedic gods and carried 
away a rich booty. These 3inadevas were probably the 
same who founded the cities of Mohenjodaro and Harappa 
and lived also in the land of the seven rivers (the Punjab). 

In the Mahabharata again we have many references 
which show that Raksasas, the Asuras and the Aryan 
Hindus had their Kingdoms side by side. In the Vana 
parva or the Book III of the Mahabharata, Chapters 13-22 
give us a description of the destruction of the Saubha Purl 
by Krsna. This may mean the destruction of a city like 
Mohenjo-daro. I mention the above references with which 
I came across in my chronological survey of the Vedas and 
the Mahabharata. They have been noticed by others 
before me, but furnish no data for any chronological finding 
% b astronomical methods. 



Date of Rama or Rama Story 

In the present work it has been ascertained that the date 
of the Bharata battle is 2449 B.C. It may now be asked 
"is it possible to find the time of Rama astronomically?" 
The answer I have to give is a definite "no." If the Puranic 
dynastic lists may at all be thought reliable, in the Vayu 
Parana (chapter 88), we have, between Rama and Brhad- 
vala, a reckoning of 28 generations till the Bharata battle, 
and the Matsya Purana (chapter 12) records 14 generations 
only, while the Vismi Purana records 33 generations 
between Rama and Brhadvala, If we put any faith in the 



siv ANCIENT INDIAN CHRONOLOGY 

Vayu list the time of Rama becomes about 700 years prior 
to the date of the Bharata battle, i.e., about 3150 B.C. 

It may be asked why have I not attacked the problem 
of finding Rama's time from the horoscope of his birth 
time given in the modern Ramayana ? The problem was 
dealt with before me by Bentley in the year 1823 AJD. and 
his finding is that Rama was born on the 6th of April, 
961 B.C. 1 a result which is totally unreliable. 

(1) The 12 signs of the Zodiac spoken of in the 
Ramayana in this connection, were not introduced in Indian 
astronomy before 400 A.D. 

(2) The places of exaltation of the planets were settled 
only when the Yavana astrology came to India of which 
also the date can hardly be prior to 400 A.D. 

(3) Bentley's finding also does not give us the positions 
of Jupiter and Mars as stated in the Ramayana reference. 

(4) The Ramayana statement of Rama's horoscope is 
inconsistent in itself. Five planets cannot be- in their places 
of exaltation under the circumstances mentioned therein, 
as the sun cannot be assumed to have been in the sign 
Aries. This ought to be clear to any astrologer of the 
present time. 

(5) Bentley has not established a cycle for the re- 
petition of the celestial positions, or has not even shown 
that his was a unique finding. Even then, as stated 
before, his finding is not satisfactory, and admitted as such 
by himself. 

(6) Further the discovery in India of the seven c planets' 
could not have taken place within the truly Vedic period, 
i.e., from 4000 B.C. to 2500 B.C. 



1 Bentley's Hindu Astronomy, page 13. L. D. Swami Kannu Pillai in his work 
11 An Indian Ephemeris," pp. 112-120, having assumed that in Rama's horoscope, the 
sun was in Aries, moon in Taurus, Mars in Capricorn, Jupiter in Cancer and Saturn 
in Libra, arrived at the vear 964 B.G., and the date as March 31 of tbe year. This 
is also impossible as calculations are^based on the S. Siddhanta, He also believes 
that Kama's horoscope was unreal. 



INTEODUCTION x. 

In the Vedic time only four of the ' planets ' were discover- 
ed, viz . , the sun, moon, Jupiter and also perhaps Venus. The 
planet Venus was very probably known by the names Vena, 1 
Vena 2 or the Daughter of Sun (i.e., ^ra ^f%?n 8 or ^rT 4 ) 
who was married to Moon, and the ASvins carried her in 
their own car to the groom.' At the time of the Bharata 
battle, however, we find that Saturn was discovered and 
named but confounded with Jupiter. Mars is called a * cruel 
planet - but not given a name. Even Mercury is named as 
the " son of Moon." (vide pages 80-32). When in later 
times 5 (i.e., later than 400 A.D., probably), the sacrifices 
to the ' nine planets ' were instituted, the appropriate 
verses selected for offering libations to these ' planets ' were 
rcas (1) " ^rr IP^fj etc.", for the sacrifice to the sun from 
the 5gveda 4 (2) " iimi4<d, etc.", for the sacrifice to the 
moon and it is sacred to the moon or soma, (3) " ' 



:, etc.", for Mars, which is sacred to Agni or fire-god, 
(4) "sr^f^w^W., etc.", for Mercury, which is also sacred 
to Agni, (5) " STSWI MR<?W ?$T, etc.", for Jupiter which 
is sacred to Jupiter, (6) iptf t srarcj, etc.", for oblations to 
Venus and this is sacred to Pusan, (7) T i&ft ^\ e etc/', for 
oblations to saturn, but the re itself is sacred to the water 
goddess, (8) "3EIT*rf^r, etc.", for oblations to the as- 
cending node, and which is sacred to Indra and (9) '* ifof 
a<*cM for the descending node's oblation and is also sacred to 
Indra. It is thus clear that the appropriate rcas for 
oblations to Sun, Moon and Jupiter only could be found 
from the Vedas : as to the rest of the ' planets * $e 
suitable rcas for offering oblations to them, could not be 
found out from the same source. 

Thus in the truly Vedic period there is no evidence 
forthcoming which would show that the ' planets Mercury, 
Mars, Saturn and the Moon's nodes were discovered.' Late 

l M.I, 14, 2, 2 M. X. 8-23,1. * M.I, 116, 17. 



xvi 



ANCIENT INDIAN CHBONOLOG? 



Mr. S. B. Dikshita's finding on this point is also the same 
as mine and the reader is referred to his great work T\flW 
I, pp. 63-66. (1st Edn.). 



, . -. .- 

Hence the conclusion is inevitable that when we meet 
with a statement like the above as to the horoscope of the 
birth time of Rama or of Krsna, we can never believe it 
It is a mere waste of energy to try to find the date of birth 
of Rama or of Krsria from such a statement, which is 
tantamount to saying that ' whenever a great man inborn 
four or five planets must be in their exalted positions. In 
scientific Chronology such " poeto -astrological eftusions 

cannot have any place. 

If we want to find the time of Rama or of Krsna, we 
have to depend on a well established date of the Bharata 
battle, and then from Puranic or other evidences try to find 
these t imes . We have already said that if the Aw* 
dynastic list can be believed, the time of Rama should be 
about 3150 B.C. 

Date of Krsna's Birth 

Similarly if we believe in the statement that Krsna was 
born on the last quarter of Sravana, on which the moon 
was conjoined with the Rohinl (AUeU-ran), then using 
the further condition that the Bharata battle was fought in 
2449 B.C., we can show that Krsna was born on July 21, 
2501 B.C. For on this day at G.M.N. or 5-8 P.M. 
Knruksetra mean time : 



Mean Sun=9821'49" 

Moon=35951'16 
Lunar Perigee =22231'53" 



A. Node = 3352'44 
Sun's Apogee = 2610' 48'' 
Sun's eccentricity =..-01834612 



Thus 
Apparent Sun=9623' 
Moon =4 50' 



INTRODUCTION xvii 

The moon was conjoined with Aldelamn about 10-34 P.M. 
Kuruksetra mean time, the moon had a south latitude 
'2 30' and Aldebaran's south latitude was 5 c -28'. The moon 
and Aldebaran were separated by about 3 C only. Thus at 
midnight the conjunction of Moon with Robin! (Aldelaran), 
was a beautiful phenomenon to observe. 

If, however, we pin any faith in the following statement 
as to the horoscope of Krsna's birth-time as it is given in 
a work on Jyotisa (Astrology) named 






WIT 



" In the places of exaltation were the moon, Mars. 
Mercury and Saturn, the ascendant was in the sign 
Taurus and Jupiter was in the place called lublia (i.e., TW, 
the eleventh house, the sign Pisces); in the signs Leo, 
Libra-and Scorpion were respectively the Sun, Yenua and 
the Node ; it was midnight and the day of the 8th tilfct on 
a Wednesday, and the moon's naksatra was Rohini-it was 
at this instant that the " lotus-eyed person named Srlkrna 
was born, and that was the great Brahman itself. -We 
readily recognise that this statement was a pure invention by 
an astrologer of times much later than 40U AD. 

Bentley attempted a solution of tin. problem of findmg 



signs of the Zodiac in Kr W a's time 
of the days of the week did n ot . ^ vogue 



' Hindu Astronomy, page, 91. 
C 1408B 



xviii ANCIENT INDIAN OHBONOLOGY 

in India much before 484 AD. 1 Thirdly the assignment of 
the houses of exaltation to the different plauots cannot be 
prior to 400 A.D. The statements of the type quoted above 
are pure astrological concoctions, having absolutely no 
chronological bearing, 

Vedic Ritual Literature 

On this bead we have (1) the Brahmnna,^ (*J) the 
Sutras, (3) Grliya Sutras and (1) the Vi'dMitfrtS. 
works cannot be of the same antiquity as the Yedas. 

As to the Brahmanas, they almost all were 
after the time of Janamejaya Pariksita, without any shade 
of doubt; the Aitareya, 2 Satapatha :{ and the (lopathii 4 
Brahmanas speak of the Asvamedlm sacrifices performed 
by this prince- From what has been shown before Jnnmne- 
jaya Pariksit a*$ time should be about ii-li;W:'J89 B.C. as 
Pariksit lived up to the age of fit) yearn and was <TOvviu*d 
king, 36 years after the Bharata battle. The oldenf 
traditional solstice days as recorded in the BrftimuuiaH 
are such as indicate an antiquity of 3550 B.C., and that the 
Yajurveda was completed about the time of the PawJavuK 
i.e., 2449 B.C. 1 The oldest tradition about the winter 
solstice day was the full-moon day of I'hiiltjuna, the next 
tradition about the winter solstice day was the mwmtxm 
day of Magha. In later times the day of full-moon of 
Phalguna came to mean the beginning of npring as in 
the Satapallw and the Taitliriya Kialimw*. The 
date when this was the case has been shown as 75<i B.(J* 
as the superior limit. According to the finding in the 
present work, the date of the Jaiminlya Braltmana has come 
out as about 1C25 B.C., the tiUmkhyilyana Brulnntmaiw* 
distinctly separate from the Kaittitaki Ilmhmana, which bun 



INTEODUCTION xix 

not been brought to light yet) as about 1000 B.C. the 
Vedangas about 1400 B.C., the Baudhayana $ ran la Sutras 
as about 900 B.C., the Apastamba and Kaiyayana Srauta 
Sutras about 625 B.C. These will be found detailed in 
Chapters XV to XX. 

In the present work, it has been shown l that the Vedic 
Hindus could find accurately the winter or the summer 
solstice day. For this the observation of the sun's ampli- 
tude at sunrise most probably used to be begun before 
the dawn. With this method came the invariable conco- 
mitant of the observation of the heliacal rising of prominent 
stars at the beginning of the different seasons. Thus in 
the earliest Vedic times, the heliacal risings of the A fains 
was found as the beginning of spring, and that of the 
Maghas as the beginning of the rains. 2 Some centuries later 
the heliacal rising of X, Scorpionis was used as a mark for 
the beginning of the Indian season of Dews (i.e., Hemanta). 
The Jaiminlya and the Tandya Brahmanas speak of the 
heliacal rising of the Delphinis cluster on the winter solstice 
day and the tfamkhayana Brahrnana of the heliacal rising 
of Pollux, at the middle of the year or the summer solstice 
day. In the present work I have generally avoided the 
use of statements like ** Krttikas do not swerve from the 
east" 3 or that the A fains were indicative of a direction. 4 
There are many things to be considered in this connection : 

(1) whether the statements mean the true eastward direction, 

(2) at what altitude did the Krttikas or A fains show the 
eastward direction. (3) what was the latitude of the 
observer. It is of course easy to see that ^ Tauri the chief 
star of the Krttikas and a Arietis of the A fains 9 had their 

1 Chapter XIII. la the reference quoted in this chapter the method of the 
Brahmana refers directly to the summer solstice day, on which the goda raised up 
the sun to the highest limit on the meridian. 

* Vide Chapters IV V. 

3 Satapatha Brahmana, II, 1,2, 8. 

* Ugveda. M. 1. 110, 3-5. 



xx ANCIENT INDIAN CHBONOLOGY 

declinations == Zero, respectively at 3000 B.C. and 2350 B.C. 
very nearly ; but these statements cannot yield a solution 
of the chronological question involved. 

In the section of this work on the Indian Eras, the 
main results have been already stated. One point of very 
great importance has been brought to light in the Chapter 
XXV, on the Gupta era. The Indian years before the time of 
Aryabhata I, were generally begun from the winter solstice 
day, but after his time gradually the years came to be 
reckoned from the vernal equinoctial day. In the Gupta 
era, the years were originally of Pausa Sukladi reckoning, 
but after the year 499 A.D,, some year of this era which 
was different in different localities, began the Caitra SukU 
reckoning. Thus one year was a " year of confusion" in 
Indian calendar which consisted of 15 or 16 lunations. The 
Caitra Sukladi reckoning was thus a creation of Arya- 
bhata I, and all works which show Caitra Sukladi reckoning 
cannot be dated earlier than 499 A.D. 

Limitations to the Astronomical Determination 
of Past dates. 

In finding the date of the Bharata Battle, the data 
evolved from the Mahabhdrata were really (1) that the 
year in our own times similar in respect of luni-solar-steller 
aspects to the year of the battle, was the year 1929 A.D. 
and (2) that the day on which the sun turned north in the 
year of the battle corresponded in our time to Feb. 19, 
1930 A.D. From these data it was quite possible" to arrive 
at the year 2449 B.C. as the year of the battle, but still we 
could not be sure that this was the real year of the battle 
unless there was a tradition to support this finding. From 
a strictly astronomical view point the year arrived at might 
be raised or lowered by one or two multiples of the 19 year 
cycle. Here the astronomical finding got a corroboration 



IlSTIKODUCTION 



xxi 



Similarly we could not be sure that the antiquity of tbe 
Vedic culture is to be dated about 4000 B.C., unless we bad 
another event of the solar eclipse as described in the 
Eg-Veda which according to my interpretation happened in 
3928 B.C., on the 26th July the summer solstice day. 
Here also we have got other traditional evidences from the 
Vedas (specially from the Atharva-Veda) and also from our 
calendar on the date for the hoisting of Indra's Flag. 3 

In Chapter XVIII on the time references from the 
Baudhayana Srauta, Sutra, according to the data which I 
could evolve from this work on the position of the solstices 
aad from the rules for beginning the Naksatresti, PaHca- 
saradlya, and the Rdjasuya sacrifices, the date has come out 
to have been 887-86 B.C. If the position of the solstices as 
indicated in the work and as understood by me is only 
approximate, the date may be raised or lowered by some 
luni-solar cycle in tropical years. If this work, the Baudha- 
yana had in addition an account of a solar eclipse on a fixed 
day of the year, we could absolutely fix the date. It was 
thus possible to fix & mean date only, for the time when the 
data evolved were astronomically correct. 

Speaking generally, an astronomically determined past 
date from luni-solar data can hardly be absolutely correct, 
when it is further recalled that there might be errors of 
observation. Lastly we have to settle whether what we get 
as the date ascertained is to be taken as the date of the work 
or the date of the tradition. Astronomy therefore can only 
give certain landmarks, as it were, in ancient Indian Chrono- 
logy, some of which should be subjected to critical examina* 
tion by epigraphic and other scientific methods that may be 
discovered and applied to test the findings in this work. 
Astronomical Constants used 

So far as the astronomical calculations and the findings 
ar*e concerned, I trust that they are correct to the degree of 



ttii ANCIENT INDIAN CHRONOLOGY 

accuracy aimed at, as in this work the most up-to-date 
astronomical constants have been used throughout. They 
are for the epoch Greenwich mean noon on January 1, 1900 
A.D. and t stands for Julian centuries elapsed from the 
epoch. Here 

L denotes tha mean longitude of a planet 
CD ,, ,, longitude of its perigee or perihelition 
e ,, eccentricity of the orbit 
# M longitude of the ascending node of the 
orbit. 

(a) For the sun's mean elements : 

L =* 28040' 56"- 37 + 129602768"' 13t + l"'089i 2 
6>2S1 13' 15"-17 + 8189 // -034 + r-63i 2 -hO' / '012t 3 
e = 0m675104-0*00004180-0'000000126 2 

(Newcomb) 

(b) For the moon's mean elements : 

a = 28336' 46 ;/ *74 + 17 '32564406 "'06 1 + 

7' / '14t 2 +0'"0068t 8 

o) 3344G' 27 f/ '4B + 14648522' 52t - 37 A/ ' 17 1 2 - 0^045t 3 
^259 T 49'16-69629ir-23t + 7^48t 2 + ;/ '008i 8 

(Brown) 

(c) For Jupiter's mean elements : 

L=238 I 9 56 f/ -59 + 10930687' / '148i + r / -20t86t 2 

;/ *005926t 8 

6> 1243' 15' / '50+5795 // '862t + 3'80258i 2 -0'01236t 3 
e = 0-04833475 + 0'000164180i - 0"'0000004676 2 
-0'0000000017i 8 

(Leverrier and G-aillot) 

For the mean elements of Mercury, Venus and Mars, 
Newcomb's and Ross's equations have been used, while 
those for Saturn, the equations used are of Leverrier and 



INTEODDOTION xrii! 

For finding the apparent places of the sun, only the 
equation of apsis has been applied, and for the apparent 
places of the moon only 4 or 5 of the principal equations 
have been applied generally. In the case of the solar 
eclipses, the mean place of the moon has been corrected by a 
maximum of 15 equations. The planetary perturbations 
have not been considered. 

Methods of chronology employed 

The methods of chronology employed in the present 
work will, I hope, be readily understood by scholars who are 
interested in this new science. In this general introduction 
it seems rather out of place to detail them. These methods 
have developed in me as the necessity for them was felt. 
Those of my readers who feel any special interest for them, 
will find them fully illustrated throughout this work and I 
would specially refer them to the sections on the Date of 
the JBharata battle and on the Vedic Antiquity. I cannot 
persuade myself to think that I am the first to discover them. 
In outline they are : 

(1) Employment of the luni-solar cycles of 3, 8, 19 160 
and 1939 sidereal years 1 as established in this work. 

(2) Methods of backward calculation of planetary 
elements from Jan. 1, 1900 A.D., G. M. Noon. 

(3) Method of finding the past time when two selected 
stars had the same right ascension (where possible). 

(4) Method of finding an eclipse of the sun in any past 
age which happened on a given day of the tropical year. The 
eclipse-cycles established are of : 

456, ,391, 763 tropical years and others derived from 
them. 2 

1 The luni-solar cycles ia tropical years will be found in Chapter IX on the 



xxiv ANCIENT INDIAN CHRONOLOGY 

For finding a solar eclipse near to a past date I have also 
found the following cycles in the way in which the Baby- 
lonian Saras is established in astronomical text books. 

They are : 

(1) 18 Julian years+10*5 days (the Chaldean Saws.) 

(2) 57 Julian years + 324'75 days. 

(3) 307 Julian years + 173*25 days. 

(4) 365 Julian years + 132'75 days. 

(5) 1768 Julian years + 388 days. 

In terms of civil days these cycles are respectively of 
6585, 21144, 12305, 133449 and 646100 days. 

These may prove useful to future researchers in chrono- 
logy, besides the ones stated before. 

For facilitating calculations according to the Indian 
Siddhantas, the following equations true for the Ardha- 
ratrika system, will be found very useful : 

(a) Surya Siddhanla Ahargana (from "creation") 
Julian days + 714401708162. 

(6) Kali Ah&rgana + 588465 -* Julian days. 

(c) Khandakhadyako, A harg ana +1964030= Julian days* 

The luni-solar cycles according to the constants of the 
Surya-siddhanta, the Khandakhddyaka and the Kryabhatlya 
are -the following : 

3, 8, 19, 122^26^385 and 648 Indian solar-years. 

Mr., Nirmalchandra Lahiri, M.A., has worked as my 
research assistant during the preparation of this work, under 
the arrangement made by the Calcutta University as detailed 
in the preface. He has revised- all my calculations, has 
made independent calculations according to my direction 
and has helped me occasionally with valuable suggestions. 

I shall be grateful for any corrections and suggestions 
for the improvement of this work. 



SPECIAL NOTE TO CHAPTER VI 

In * this work in finding the past dates by the heliacal 
risings of stars at different seasons, the author was 
under the impression that the Vedic Hindus were more 
concerned with the beginning of the dawn than with the 
actual heliacal rising of the star concerned." It is for this 
reason, that it has been assumed throughout, that the 
sun's depression below the horizon was 18, when the star 
was observed near the horizon and not at the exact heliacal 
visibility, which might have happened some days earlier. 
On the other hand it may be held that in some cases at 
least the actual heliacal visibility itself should have been 
taken as the basis for the determination of the dates. This 
of course may be conceded. In the case of the brightest 
star, viz., Sirius or a Ganis Majoris, the correct depression 
of the sun below the horizon at its heliacal visibility should 
be about 10. The Vedic people were perhaps not so very 
accurate in their observation. Hence in the case of this 
star, the sun's depression below the horizon should be taken 
at 12 and not 10 at its heliacal visibility. This would 
allow for the necessary altitude of the star above the horizon 
at the time of observation so that it might be easily 
recognised. This would also allow for the uncertainty of 
the horizon being clear for observation. 

In view of the above consideration the finding of the 
date of Vamadeva in Chapter VI, should be modified. Again 
Vamadeva's statement that the Rbhus should awake since 
12 days have elapsed in their period of sleep in the orb of the 
sun, may or may not be associated with the heliacal rising of 
the Dogstar as spoken of by Dirghatamas. If this association 
is- not allowable Vamadeva's date cannot be found 'on this 

D-I408B 



xxvi ANCIENT INDIAN CHRONOLOGY 

basis. If this is allowed, it may be assumed that the 
summer solstice day was probably estimated from the 
correct determination of the winter solstice day. 

It thus becomes necessary to determine by how many 
days did the estimated summer solstice day, precede the 
actual summer solstice day. It has-been shown on .-page 
108, that at about 2000 B.C. the sun's northerly course 
lasted for 186 days, while the Vedic people held that the two 
courses were of equal duration, each' having a length of 
183 days. The estimated summer solstice day would be 
3 days before the actual summer solstice day. Hence 
Vamadeva' s statement of 12 days after the summer solstice 
day as estimated would mean a day 9 days after the summer 
solstice day. The sun's longitude should be taken about 
99 and not 102 as used in Chapter VI. The sun's 
depression below the horizon should be 12, and o>, the 
obliquity of the ecliptic at 2100 B.C. -2356'15*. 

Hence sun's right ascension = 9949'52". the sun's 
declination=2327'30". It would follow that : 

(1) ZPS12Q58'9" 3 (2) yE = 68ol'43", (3) the angle 

= 5417'21", (4) yO = 849'24", (5) OL=3628'22" and 

(6) yL = 4740'52" as shown and named in the figure in 

page 87. Sirius'^ mean longitude for 1931 being 1038 / , the 

increase in the longitude of the star till 1931 becomes 5527', 

which showa the date of Vamadeva to be about 2100 B.C. 

This seems to be a result hardly acceptable. Vamadeva in 

the Bgveda, M. IY, 15, in verses 7-10 invokes the fire-god 

Agni to bless the Kumara Sahadevya (son of Sahadeva) 

whose name is Somaka. According to thePuranas, Sahadeva, 

the son of Jarasandha, was killed in the Bharata battle, and 

his son, the grandson of Jarasandha was Somadhi. If 

Somalia and Somadhi mean the same prince, the date of 

Vamadeva should be about 2449 B.C., which is the date of 



SPECIAL NOTE TO CHAPTER VI 

ascending l brilliant emblem of Agni (i.e., Krttikas) as 
stationed on the east of the earth (M. IV. 5, 7). Assuming 
the star Alcyone of the Krttikas was seen at Rajgir (25N) 
at and at an altitude of about 730' (or 8 due to refraction) 
on the prime-vertical, the date comes out as MM B.C . At 
this altitude also the swift ascending stage may be admitted. 
It is quite unintelligible, how Prof. Prey, from the same 
data assumed that the star was on the prime-vertical at an 
altitude of 30 and thus arrived at the date 1100 B.C. 
(Winternitz's History of Indian Literature, Vol. I, page 298). 
The heliacal visibility of the star is really indicated by 
what rsi Dlrghatamas says ; we may therefore try to 
determine the date of Dlrghatamas. It is the tradition of 
N. India, that the cloudy sky persists for 3 days after the 
summer solstice day, the period being called ambuvacl or 
cloudy days. We therefore take the following data for the 
heliacal visibility of the Dogstar in Dlrghatamas 's time : 

(a) Sim's longitude =93, ,(&) the sun's depression below 
the horizon at the heliacal visibility of the star = 12, (c) the 
obliquity of the ecliptic =24!' for 2900 B.C., '(d) the 
latitude of the station, Kuruksetra==30N. 

Now the sun's right ascension a =9317 / , the sun's 
declination 2358'54". We calculate as before 

(1) Z.ZPS12118'16", (2) r E = 6158'44", (3) LO 
-5129 / (4) y O7741'7", (5) OL419'46" and (6) yL 



Translation : 

" May our self-purifying praiae, suited to his glory, and accompanied by worship, 
quickly attain to that omniform (Vaifvanara) whose swift ascending brilliant (orb) la 
stationed on the east of the earth, to mount, like the sua, above the immovable 
heaven," 

Here in place of " orb " as supplied by Wilson, the word should have been 
"emblem" i.e., the Krttikas (Pleiades) of which the regent is the firegod 
Vaitvanara or Agni. He nee is our astronomical interpretation, which is echoed in 

&e$atapatha Bralimaya, Kan$a> II, Oh,, 1, 2-3, that the Krttikts do not swrve 
from the east. 



- ANCIENT INDIAN CHEONOLOGY 

36 31'21", (7) the increase in the longitude of Sirius till 
1931 = 6677' nearly. The date arrived at for Dlrghatamas 
becomes 2926 B.C. 

Now the date of the Bharata battle as found in this 
work has been 2449 B.C. This rsi Dirghatamas was a 
contemporary of King Bharata of the lunar race according 
to the Aitareya Bralimana. 1 Between Bharata and 
Yudhisthira the dynastic list of the lunar race as given in 
the Mahabharata (MBh., Adi, Chapter 95), records 17 reign 
periods of princes of this dynasty. The interval between 
the dates stated above is 476 years, which divided by 17, 
makes the average length of a reign period 28 years. 
Hence the historical method here corroborates the astronomi- 
cal finding. 

As to the remaining findings in this work on the basis of 
seasonal heliacal risings of stars, perhaps Deed no modifica- 
tion specially when the stars are ecliptic and also when 
they are of a magnitude less than the second, 

1 - Aitareya Bra7ima#a, Ch. 39, Khanda 9, 22. 



"By this Aindra great anointing, Dlrgbatamas, the son of Ma rnata, bathed tlie 
King Bharata, the son of Dusyanta. By virtue of it Bharata, the son of Dnsyanta, 
conquered the whole world in. all the quarters in his victorious expedition and also 
performed the A4vamedha sacrifice " 

C/. also Satapatha Brahmatia, Ch. 18, 5, 4, 11-14. Weber'a Edn., p. 95. Here 
no mention is made of the priest Dirghatamaa* 



ANCIENT INDIAN CHRONOLOGY 

CHAPTER I 

DATE OF THE BHARATA BATTLE 
Evidence from the Mahabharata 

The Bbarata battle is now generally believed to have been a 
real pre-historic past event. It is on this assumption that we 
propose to determine the date of this battle. Hitherto no epigra- 
pic evidence leading to this date has been brought to light. 
Consequently we have to rely on our great epic the Mahabharata 
and the Puranas. The description of the fight can be found only 
in the Mahabharata while the Puranas de6nitely indicate that it 
was a real event. In this chapter we rely solely on the Mahabha- 
rata astronomical references. The great epic Mahabharata has 
had its development into the present form, from its earliest 
nucleus in the form of gdtha naragarhsis, i.e., sagas or songs of 
heroes. In fact the Mahabharata itself is jaya or a tale of victory, 
so also are the Puranas. The next stage in the development of 
the Mahabharata was perhaps in the form of the works Bharata 
and the Mahabharata as we find enumerated in the Afoalayana 
Grhya Sutra (III, 4, 4). The jbresent compilation began from 
about the time of the Maurya emperors. There are in it mention 
of the Buddhist monks and the Buddhists in several places. 1 
Again one astronomical statement runs thus : 

" First comes the day and then night, the months begin from 
the light half, naksatras begin with Sravana and the seasons with 
winter." 2 



3 Book I, Oh. 70 : titarafNr$4ta 3*RtKi1lfecHi 288'J of di Pana ; 
Book V3I, Cb. 45, St. SO, ^hich runs thus : 



ftr: t Also Book XII, Ch. 218, Stanza 31, etc., contains the Buddhist 
doctrines of rebirth. Asiatic Society Edition of the MahabMrata. 



Afonmedlia, Ch. 44. St, 2 



2 ANCIENT INDIAN CHRONOLOGY. 

In 1931 A.D., the celestial longitude of 3ravand (Altair) was 

300 48' 9". According to the modern Stirya Siddhdntd, the polar 

longitude of this star is 280, l while Brahmagupta in his Brahwa- 

sphuta Siddhdnta quotes its earlier polar longitude as 278 .* 

Hence according to the former work, the star Sravana itself marks 

the first point of the naksatra and according to the latter, the 

naksatra begins at 2 ahead of the star. The Maliabharata stanza 

quoted above shows that the winter solstitial colure passed through 

the star Altair (Sravana) itself or through a point 2 ahead of it, as 

the season winter is always taken in Hind a astronomy to begin 

with the winter solstice. The passage indicates that winter began 

when the sun entered the naksatra fSravand. It shows that the 

star Altair had at that time a celestial longitude of 270 or 268, 

the latter according to the BrdhmaspJiuta Siddhdnta. The 

present longitude of Altair may be taken as 301 nearly. The 

total shifting of that solstitial point has now, therefore, been 31, 

which indicates a lapse of time = 2232 years. This n eans the 

epoch to be the year 297 B.C. If we accept Biahmagupta's 

statement for the position of this star, the date is pushed up to 

441 B.C. Hence there is hardly any doubt that the MahdbMrata 

began to be compiled in its modern form from 400 to 300 B.C. 3 

Before this as we have said already, there were known two books 

the BMrata and the MalidbMrata as mentioned in the 

Asvaldyana Orhya Sutra. 4 The great epic, as we have it now, 

has swallowed up both the earlier works, and the oldest strata in 

it can be found with great difficulty. The present book is in itself 

in the most discursive form. Whenever a topic is raised, it is 

dilated in a way which is out of proportion to the real story of the 

Pandava victory. In this way some of the stanzas of the old saga 



ya SiddMnta, vinV4. 

2 mftser'ft: i 

Brahmatplwta Siddhdnta, Ch. X, 3. 

3 Cf. S. B/Dft?ita*s n*^ afift:*tra, P- ni 2nd edition. He estimate th* 
date at 450 B.C. 

4 



Atvalauana Gr'hya Sutra, Ch. 3, 1C, 4, Sutra 4. 



DATE OK THE BHARATA BATTLE 3 

% 
have got displaced from their proper settings, as many details 

came to be woven often uncouthly, into the story. 

The Time References from the Mahabhdrata 

We shall now try to set forth some of the time references as 
found in the present Mahabhdrata which we understand to be the 
oldest, and which lead to the determination of the year of the 
Bharata battle. 

In these references quoted below, the days are indicated by the 
position of the moon near a star. No mention of tithi is made. 
We shall have the distinct references to the Astakas, Amavasyds 
(not amfivasya* or the period of moon's invisibility, and Paurwa- 

masis. 

Naksatras in these references mean most probably single-stars 
or star groups. In late* times of the . Vedangas there are indeed 
recognised 27 nakwlras of equal space into which the ecliptic was 
divided, but we do not know the exact point from which this 
division was begun. It is, therefore, safer to take the nahsatras 
to mean atars or star groups in this connection. 

The Mahabhdrata astronomical references which we are going 
to use for determining the year of the Bharata battle, are casual or 
incidental statements, Und as such do not directly state the time or 
the portion of the equinoxes or the solstices of the year in which 
the event happened/ They state firstly the moon's phases near to 
several stars at some of the incidents of the battle and secondly 
indicate the day on whifh the sun reached the winter solstice that 
year. We state them as follows: 

<j> In the Vdyotja Pan* or Book V, Oh. 142, the stanza 18 

runs a follows : - 

' From the seventh day from to day, there will be the period 
of the moon's invisibility ; BO begin tbe battle in that, as its 
presiding deity has been declared to be Indra.' l 

This in taken from the speech of Ersna to Karna at the end 
of his unsuccessful peace-mission to the Kaurava- court. It means 



4 ANCIENT INDIAN OHBONnLOGY 


that before the battle broke out there was a new-moon 

near the star Antarea or Jyestha of which the presiding deity is 
Indra, As invisibility of the moon was taken to last two days, 
and only one presiding deity is mentioned, this presiding deity 
Indra, shows the star Jyestha near which happened the new- 
moon. This new-moon marked the beginning of the synodic 
month of Agrahdyana of the year of the battle. 

Again from the fifth case-ending in ' saptamdt,' 'from the 
seventh day from to-day ' shows that when the speech was made, 
the Astakd or the last quarter of the current month of Kdrttika 
was just over. At the mean rate the moon takes about 7*5 days 
to pass from Regulus to Antares. Hence in the latter half of 
the previous night the straight edge of the dichotomised moon was 
probably observed as almost passing through the star Regulus. 
This formed the basis of this prediction of the coming new-moon. 
The moon's invisibility was thus to begin from the 7th day and 
last till the day following, We further learn that while Krsna 
was negotiating for peace at the Kaurava Court, there was a day 
when the moon neared the naksatra Pusyd (8,73,7 Cancri) group, 
from Duryodhana's command which was thus expressed: 

" He repeatedly said * march ye princes, to Kuruksetra ; 
today the moon is at Pusya.'* 1 

The day on which Krsna addressed Karna was the fourth day 
from that day. 

Hence in the year of the battle, the last quarter of Kdrttika 
took place near the star Regulus and the next new-moon near 
the star Antares which marked the beginning of the lunar month 
of Agrahdyana. But the battle did not actually begin with this 
new-moon. For on the eve of the first day of the battle Vyasa 
thus speaks to Dbrtarastra : 

(ii) " Tonight I find the full moon at the Krttikds (Pleiades) 
lustreless, the moon became of a fire-like colour in a lotus-hued 
heaven. " 2 



n 



M. Bfc., Bfcitfma Parva or BK, VI, Ch. 2, 23. 



DATE OF THE BH1UATA BATTLE 5 

If there be a new-moon at the star Antares, the next full- 
moon cannot be at the star group Pleiades. At the mean rate 
the moon takes exactly 12 days 23 hours or about 13 days to pass 
from the star Antares to Pleiades. The moon was about 13 days 
old and not full. Vyasa by looking at such a moon thought the 
night to be Paurnamdsl no doubt, but it was of the Anumati 
type and not of the type J?afea, which was the next night. 
There are other references to show that the moon could not be 
full on the eve of the first day of the battle. 

On the fourteenth day of the battle, Jayadratha, Duryo- 
dhana's brother-in-law, was killed at sunset ; the fight was 
continued into the night, and at midnight the Rdksasa hero 
Ghatotkaca was killed. The contending armies were thoroughly 
tired and slept under truce on the battle-field itself. 2 The fight- 
ing was resumed when the moon rose sometime before sunrise. 
How and when the fight was resumed are described in the 
following way: 

(Hi) *' Just as the sea is raised up and troubled by the rise of 
the moon, so up-raised was the sea of armies by the rise of the 
moon, then began again the battle, -0 King, of men wishing 
blessed life in the next world for the destruction of humanity." 3 

As to the time when the fight was resumed we have the 
statement : 



1 



Aitareya Brahmana, Cli. 32, 10, 



2 ^rf Kifa: ^fusra" Pnswirt ftS^rcf; i 
TO T 



M. B/i., Drowa, Cb. 185. 

: ^jftra: 



M. Bli.> Drorifl, Ch. 185. 



G ANCIENT INDiAS CHBONOLOGY 

(iv) " The battle was resumed when only one-fourth of the 
night was left." 1 

Here * one-fourth * must mean some small part as we cannot 
think that they could exactly estimate * one-fourth of the night.' 
Thus the moon rose that night when only a small part of it was 
left, and the description of the moon as it rose was 

(t?) " Then the moon which was like the head of the bull of 
Mahadeva, like the bow of Cupid fully drawn out, and as pleasant 
as the smile of a newly married wife, slowly began to spread her 
golden rays," 2 

It was a crescent moon with sharp horns like those of a bull, 
that rose sometime before sunrise, and was 27 days old. From 
this it is clear that the Bharata battle was not begun on the 
new-moon day spoken of in our reference (i) ; and on the eve of the 
first day of the battle she was not quite full but about 13 days old . 
As has been said already the night before the first day of the battle 
was a Paurnamasl of the Anumati type it was not Rdkd. 

On the 18th day of the battle, Krsna's half-brother Yaladeva 
was present at the mace-duel between Duryodhana and Bhima. 
He just returned from a tour of pilgrimage to the holy places. 
His words were : 

(t?i) ** Since I started out, to-day is 40 days and 2 more ; I 
went away with the niooa at Pu^ya and have returned with the 
moon at ravand (Altair)" 3 

Hence on the day of the mace-duel, the moon was near to the 
atar Altair, and at the mean rate the moon takes about 18 days 
and 8J hours to pass from Alcyone to Altair. Owing to the 
moon's unequal motion it is quite possible for her to accomplish 
this journey in 18 days. Hence this passage confirms the state- 
ment made above that on the eve of the first day of the battle 



\\\\\ 

M. Bh Drone, Ch. 187. 



M. Bli.,Dron(t t Ch. 185. 



M. Bh. t iSalya t Ch.34,6. 



DATE OF THE BHARATA BATTLE 7 

the moon :was near to the star group Krttikds or Alcyone and that 
she was about 13 days old. For 

From the day of the moon at Pusija till the day of 

Krsna's speech to Karna ... ... ... 3 days 

From that day till the new-moon at Antares (Jyestha) 8 ,, 

From the new-moon at Antares till the moon at the 

Eritikas ... ... ... ... 13 ,, 

And the fight had already lasted ... ... 17 ,, 



Total ... 41 days 

The next day was the last day of the battle and was the 42nd 
day from the day when the army of Duryodhana marched to 
Kuruksetra and Valadeva started out on his tour. 

On the 10th day of the battle at sunset, Bhlsma, the first 
general of the Kaurava army, fell on his ' bed of arrows,' became 
incapacitated for further participating in the fight and 
expired after 58 days, as soon as it was observed that the sun 
had turned north. Yudhisthira came to the battle-field to see 
Bhlsnia expire and to perform the last rites. The MaMbhclrata 
passage runs thus : 

(vii) " Yudhisthira having lived at the nice city of Hastina- 
pura for fifty nights (after the battle was over), remembered that 
the day of expiration of the chief of the Kauravas (i.e., Bhfsma) 
had come. He went out of Hastinapura with a party of priests, 
after having seen (or rather inferred) that the sun had stopped 
from the southerly course, and that the northerly course had 

begun." 1 

Tt IB clear that special observation of the winter solstice day 
was made in the year of the battle, as Bhlsma was to expire as 
soon as it was observed that the sun had turned north. 
Yudhisthira started most likely in the morning from his capital 
to meet Bhmma on the battle-field. After the lapse of 50 nights 



fit 

M T Bh., Awtatana, * BE. XIII, Ch. 167 



8 ANCIENT INDIAN CHEONOLOOY 

from the evening on which the battle ended he was sure that 
the sun had turned north. Hence the day of Yudhisthira's start- 
ing out from his capital was the day following the winter aoltftic-o 
day. When Yudhisthira met Bhlsma at Kuruksetra, he (Bhfsma) 
thus spoke to him : 

(oiii) "It is a piece of good luck, Yudhisthira, the son of 
Kunti, that you have come with your ministers. The thousand 
rayed glorious Sun has certainly turned back. Here lying on my 
bed of pointed arrows, I have passed 58 nights ; this time has been 
to me as endless as a hundred years. YudhiHthira. the lunar 
month of Magha is now fully on and its three-fourths are ovtr 
This ought to be the light half of the month." 1 

Here the last sentence was a pious wish not materialised, in 
our reference (mi) '50 nights 1 and in (vih) T>H nighty" arc corro- 
borative of each other. A lapse of nights from the end of Uit* 
battle and that of 58 nights from the evening on which Bhisrun 
fell on his "bed of arrows/* both indicate the ssimc <iav, Thiev- 
fourths of Magha became over at the hint quarter or the 
Ekastakd day. The time indication is peculiarly identical with that 
of the Brahmanas. The lunar months here iu*ed are 
from the light half of the month, for reasons pot forili 

(a) Time from the new- moon ut Anhnrx to Ih** 
moon's reaching tho KrltiMx or I'lfinilt's .,, Hi <! 

Bhisma's generalship .,. ... ... lu 

Bhisma on death-bed ... >.. - M 

Total ... HI 

(b) From the rxew-moon at Anittrvn nr the heginning 

of the lunar AgraJiuyaya till its end ,,, 2U'5 i 

The lunar month of Paum ... ,,, 2UT 

f of the lunar month of Muglnt ... ... % J*J'M 



jrrSsRr 



TOT 



Bk NJH, 



DATE OF THE BHIEATA BATTLE 9 

Hence the two reckonings are corroborative of each other. If, 
on the other hand, we assume that the lunar months counted 
here were from the dark-half of the month and ending witb the 
light half, the synodic month of Agrahayana wo^ld be -.half over 
with the new-moon at Antares. From that time till $tb->of Magha 
were over, we could get only r 

(c) Half of Agrahayana ... ... .. 14*76 days 

Month of Pausa ... " ... ... 29*50 ,, 

$ of Magha ... ... ... ... 22'00 



Total ... 66*25 ,, 

number of days bere counted falls short of the 68 days 
which comprised Bhlsma'e generalship of 10 days + 58 days ID 
which he was on death bed. It is thue* evident that the lunar 
months which end with the full-moon and half a month earlier 
than the new-moon ending lunar months, are not used in these 
Mahdbhdrata -references. 1 It is also clear that the MahdbJiarata 
t-ays that Bhisma expired at sunset on the day of the last quarter 
of Mtifrha. So far as astronomical calculation is concerned, we take 
that the sun reached the winter solstice one day before the expiry 
of Bhisma, or that full 49 nights after the battle ended, the sun 
reached the winter solstice according to our reference (vii). We are 
inclined to think that in this reference a clear statement occurs as 
to the observation of the winter solstice day, no matter even if the 
reference (viii) be a fiction. 

To sum up: In the year of the Bbarata battle, there 
was the last quarter of the month of Karttika with the 
moon near about the star Regulus as we have inferred. Secondly, 
in that year the beginning of the next month of Agrahayana 

*i 

1 The original word in place of Sukla was perhaps Krsna and a. subsequent redactor 
changed the word to JSukla, to bring out the approved time for the death of Bhlsma. 
Xllakanthn, the commentator of the Mahabharata quotes a verse from the Bharata 
Savitri, which -also says that ' Bhlsma was killed by Arjuna on the 8th day of the dark 
half of the tLonth of Magha * : see Bhisma Parva, ch. 17, stanza 2. In an edition of the 
Bharata Savitri the verse runs as 'Bhisrna was killed in the month of Agrahayana 
oo the 8th day of the dark half.' This of course refers to the day on which Bhisma fell 
oa his 'bed of arrows* ; 58 days after that, i.e., exactly one day less than full two 
synodic months becomes the 7th day r of dark half of Magha. Hence also Bhisma 
expired in the dark hulf of Magha and not in the light half, 
2 -140KB 



10 ANCIENT INDIAN CHRONOLOGY 

took place with the new-moon near the star Antares or 
Jyestha, which is directly stated. Thirdly, the battle lasted 
till the moon reached the star Altair or Smvam. Fourthly, 
when *49 nights after the battle expired, the sun reached the 
winter solstice. We are to understand by the term ' Nalwatra ' 
simply a star or a star-group. W$ should also recollect that 
Bhisma expired on the day of the last quarter of M fig ha and, art 
we have understood, the sun's reaching the winter solstice took 
place one day earlier. 

From these references it is possible to determine the date of 
the Bharata battle. We shall use two methods, but the result H 
obtained from both the methods will be approximate, Tn the firt 
method we shall, for the sake of convenience, assume that the 
nearness of the moon fa. the several starts as* equivalent to wart 
equality in celestial longitude of the 'moon with thotie .s7<m?. 
With this meaning of ' nearness* wo may derive the following seta 
of data lor finding the year of the Bharata battle. 

Data for the calculation of the Date of Ihe. liharata batlU 
by the First Method 

la) There was a new-moon at the star Anlarex, before tin; 
battle broke out and the sun turned north in 80 days, i.e., one day 
before Bhisma 1 s expiry. 

(b) On the eve of the first day of the battle, the moon !.' 
days old was in conjunction with the Krttikits or Aleytme, and (lit* 
sun turned north in 10 + 57 = 67 days, 

(c) On the 18th day of the battle, moon 81 days old wan in 
conjunction with Sravana or Altair, and the nun tiirn*d north in 
49 days. 

Calculation of Dale by the First Met hud 

9 Before we can proceed with our calculation we nott* down 

below the mean celaatial longitudes of the ntars cotirenu'd for ttit* 
year 1931. 

Star Mean t'<*k*8tiul i 

Jyestha or Antares 218* 47' 

Krttika or Alcyiyn* fitf u * J' *t I* 

Sravnnu or Altuir MI* 4 t 



DATE OF THE BHAEATA BATTLE 11 

(A) From the data (a) we assume, as already stated, that the 
sun, the moon and the star Antares had the same celestial longi- 
tude at that new-moon. 

Hence the present (1931) longitude of 

the sun at the new-moon at Ant arcs -4248 4% f 57^ 

Sun's motion in 80 days ... 78 51' 6* 

Hence the mean celestial lofig. in 1931 

of the sun for reaching the winter 

solstice of the year of the Bharaja 

battle " 327 39' W (1) 



(B) From the data (6), the moon at the assumed conjunction 
with Krttika or Alcyone was 13 days old, 

HeStce the (1931) celestial longitude of 

the moon at that time was 59" 1' 44* 

The moon was 13 days old and the mean 
synodic month has a length of 
29-530588 days 

.'. " the moon was ahead of the sun by 

- 158 * <" 

,'. the sun's present day (1931) mean 

celestial longitude for that time 26U 32' 57* 

Sun's motion in 67 days ... 66 2' 18" 

Hence the present (1931) mean celestial 
longitude of the sun for reaching the 
winter solstice of the year of the 
Bbarata battle 326 35' 15" (2) 

(C) From data (c) the moon at our assumed conjunction with 
Sravam or Altair was 31 days old. 

Hence the present (1931) celestial longi- 
tude of the moon for that time 30C) 48' 9" 

The moon was ahead of the suif by 
360 x 31 



29-530588 



or ... 377 54' 



.'. the present (1931) celestial long, of 

the sun for that time ... 282 53' 21' 

Sun's motion in 49 days ... 48 17' 48* 

Hence the (1931) mean celestial longitude 
of the yun for reaching the winter 
solstice of the year of the Bharata 
battle ... 331 11' 9" (B) 



12 ANCIENT 1NU1AN CHItUNULOGY 

We thus arrive at three divergent values of the present (1931) 
mean celestial longitude of the sun for reaching the winter solstice 
of the year of the Bharata battle, viz. : 

From data (a) ... ... 327 39' 3", result (1) 

(b). ... ... 326 35' 18*, (2) 

" \,' f (c) ... ... 381 IV V, (3) 

The mean of these values = 328 28' 29" 

From the above calculations, the present (1931) mean tropical 
longitude of the sun at the winter solstice of the year of the 
Bharata battle is the mean of the results (1), (2) and (3), via., 
328 28' 29". 

Hence as a first step the total shifting of the winter ftlstice 
up to 1931 A.!D. is roughly 328 28' 29" - 270 = 58 28' 29", 
which represents a lapse 0^4228 years 1 . 

Now 42 centuries betore 1900 A.D., the longitude of the sun's 
apogee was about 29. Hence allowing for the change in the 
eccentricity of the sun's apparent orbit, the sun's equation of 
centre for the mean longitude of 270 in the year of the Bharata 
battle works out to have been + 1 51' nearly. 

Hence what was 270 of the longitude of the sun in the battle 
year, was 328 28' plus 1 51' (= 330 190 in the year 1931 A.D., 
which shows a solsticial shifting of 60 19' and represents a lapse 
of 4362 years. 

The year of the Bharata battle thus becomes near to 2432 B.C. 
This is the best result that can be obtained from our first method. 

Calculation of Date by the Second Method 

On looking up some of the recent calendars, we find that a 
new-moon very nearly at the star Antares took place on: 

(J) December 1, 1929, at 4 brs. 48'4 min. G. M. T. or at 

9 hrs. 56*4 min Kuruksetra mean time. 

* 

9 

1 Annual rate of precession = 50"' 2664 +0" 0222 T, where T = np. of centuries 
from 1900 AD. As a first appoximation, with the annual rate of 50" 25, the solstices 
take 4183 >ears to recede through 58' 27' 28". Now from the above equation the annual 
rate for 1931 A.D. is 50"* 2633, and 4188 years earlier (i.e., 4157 years before 1900 A.D.) 
it was 49'" 3335. Working with tbe mean of the two values (tiz 49" '7984) the lapse 
of years comes out to be 4*228. 



DATE OF THE BHAliATA JiATTLE 13 

The sun's longitude at G. M. midnight < r Kuruksetra mean time 
5 far*?. 8 min. A. M. v as 248 19' 10" 

The moon's longitude at that time 246 4' 24" 

The longitude of Antares 248 46' nearly 

Hence December 1, 1929 was a new-moon day, the conjunc- 
tion taking place very nar to Antares. It was the day of the 
new-moon of which the presiding deity was Indra and it was 
the beginning of the synodic monAh of Agrahayam. Thirteen 
days later was 

(2) December 14, 1929 ; at 5-8 P.M. of Kuruksetra mean 
time which corresponded with the -eve of the first day of the 
Bharata battle : 

The sun's longitude * 262 1' 57" 

The moon's longitude 54 40' 7" 

The longitude of Krttikd or Alcyone 59 nearly 

The moon came to conjunction with Krttikd in about 8J hrs. 
morp. In the evening at Kurukaetra, the moon was about 3 
behind the Krttikds visibly, the moon being affected by parallax 
due to its position near the eastern horizon at nightfall. Eighteen 
days later was 

(3) January 1, 1930 ; at 5-8 P.M. of Kuruksetra mean time: 

The sun's longitude 280 22' 2* 

The moon's longitude 296 47' 35// 

The longitude of Altair or Sravayfr 300 45' nearly 

The moon came to conjunction vnth Altair in 8 hours more. - 
This evening corresponded with the evening on which the 
Bharata battle ended. Fifty days later came " 

(4) 20jj|h February, 1930 ; the day corresponding to that of 
Bhisma's expiry. At 5-8 P.M. of Kuruksetra mean time: 

The sun's longitude 331 8' I" 

The moon's longitude 242 40' 55" 

The moon had come t > her last quarter at about l hrs. before. 



14 ANCiLNT INDIAN CHRONOLOGY 

Assuming that the sun turned north exactly one day before 
Bhlsma's expiry, as before, the true anniversary of the .winter 
solstice day of the year of the Bharata battle fell on the 19th 
February, 1930, 

On the Svening'of the 19th February, 1930 A.D., at 5-8 P.M. 
of Kuruksetra time which was the G. M. noon of that day, the 
sun's mean tropical longitude was 328 42' nearly which is in 
excess of the value obtained by the first method by 15' only. 

By a similar process shown before in our first method, we 
deduce that the sun's equation of centre for the sun's mean 
longitude of 270 in the year of the battle was +1 51' nearly. 

Hence what- was 270 in the year of the battle was 828 A2'-h 
1 51' i.e. 330 $3 in 1930 A.D. 

The total shifting of the solstices up to 1930 A.D. thus becomes 
(>(> 33' representing a lapse of 4379 years. 

The battle year should be thus very near to 2450 B.C. 

By the first method we have arrived at the date 2432 B.C., 
while our second method gives the year 2450 B.Cr We have 
now to examine if there is any tradition which supports these 
findings. 

Three Traditions as to the Date of Uie Bharata Battle 

There are at present known three orthodox traditions as to 
the date of the Bharata battle. 

(1) The firsfc of the traditions is due to Aryabhata I (499 
A.D.), who in his Dasagitikd, 3, says ' of the present Kalpa, or 
JEon, six Manus, 27 Mahayugas and three quarter Yuyas 
elapsed before the Thursday of the Bharatas ' 1 . This is a simple 
'statement that the Pandavasjived at the beginning of the astro- 
nomical Kali age or at about 3102 B.C. 

(2) c The second tradition recorded by Varahamihira (550 

A.D.) is ascribed by him to an earlier astronomer Vrddha Garga 

** 

(much earlier than Aryabhata I). Varaha says ' The seven rsis 

were in the MagMs, when the King Yudbisthira was feigning 



Dafagltika, 3. 



DATE OF THE BHAIIATA BATTLE 15 

over the earth ; his era is the era of the Saka Kings to which 
'2526 have been added ' l . The first part of this statement has 
remained a riddle to all researchers up to the present time. The 
second part gives a most categorical statement that Yttdhistbira 
became King in 2526 of Saka era, whfcb corresponds to 
2449 B.C. 

(3) Tie third tradition is due to an astronomical writer of 
the Pwanas, who says, ' Prom th,e birth of Pariksit to the 
accession of Mahapadma Nanda, the time is one thousand and 
fifty years (or one thousand fifteen years or one thousand five 
hundred years).' 2 

Now taking the accession of Chandragupta to have taken 
place in 821 B C., and the rule of the Nandas"to have lasted 
50 years in all, the birth of Panksita^ according to the statement 
of this Puranie writer, becomes abput 1421 B.C. or 1871 B.C. 

Of these three traditions our finding of the date of the Bbarata 
battle, whether 2432 or 2450 B.C. approaches closest to the 
year, -2526 of the Saka era or 2449 B.C. It is, therefore, 
necessary to examine the 5 ear, -2526 of the Saka era. 

Astronomical Examination of the year, 2526 of the Saka 
em or 2449 B.C. 

We have found before that in 1851 of Saka era elapsed or 
1929-30 A.D., the various ' conjunctions ' of the moon with the 
sun and the several stars happened in closest coincidence with the 
Mahdbhdrata references. 

From, 2526 to 1651 elapsed of the Saka era, the number of 
years was 4377. We shall assume that these were Fidereal years. 



: srrafr yetf jftrfW writ \ 

tliita, xjii, 3. 



Pargiter's Dynasties of the Kali Age, p. 58. 



16 ANCIENT INDIAN CHEONOLOQY 

Now, 

Sidereal year _ 365-25636 
Sidereal month 27-32166 



= 134- i- i_ - 



2+ 1+ 2 + 2+ 8+ 12 + 7 + 

e 

1 he successive convergents are 

IB j?7 i? 12! 254 2139 25922 

1 2 ' 3 " ' 8 ' 19 J 160 ' 1939 ' 6l/C ' 

The last three of the above convergents give the luni-solar cycles 
of 19, 160 and '1939 \ears in which the ruoon^ phases with 
respect to the sun and the st^rs repeat themselves. 

Here we have 4377 = 1939 x 2 + 160 x 4 -f 19. 
In fact we have 

Sidereal year x 4377 = 1598727-092 days 

Sidereal month x 58515 = 159872(5-993 ,, 
and Synodic month x 54138 = 1598726-978 

Thus from a consideration of the mean motions of the sun 
and the moon, it is inferred as a certainty that the various 
* conjunctions * of the moon with the sun and the stars recorded 
in the Mahabharata did actually happen in 2526 of Saka era or 
2449 B.C. Here the Mahabharata references enable us to 
construct the battle calendar ; we further, want to see how the 
various phases of the moon npar to the fixed stars happened in 
the battle-year on the days stated, and how the winter 
solstice" d ty stood in the year in relation to the day of Bhisma's 
expiry. 

Construction of the Battle Calendar 

It has been said before that a new moon near the star Antares 
happened in our times on December 1, 1929 A.D., which we have 
taken to have been more or less exactly similar to th&t which 
happened in the year of the battle. 



DATE OF THE BHABATA BATTLE 
Now Julian Days on Dec. 1, 1929 =242^947 

less no. of days in 54138 synodic months =1608727, OB shown al 
.'. Julian days for the required date =827220, whence 
the date arrived at is October 21, 2449 B.C. 
Now Julian day s on Jan. 1, 1900 A.D. =2415021, 
and Julian days on Oct. 21,2449 B.C. =827220 

Difference =1587801 days 

=43-47 Julian eeiiturie* 
+59-25 days. 
(1) Hence on Oct. ai, 2449 B.C. at G.M.N. 

.*. apparent Sun188 c 4G', 



Mean Sun =18925'45".15, 

,, Moon =191 18' 4".25, 

Lunar Perigee = 18826'44"*75, 



A Node =103 9'58" 75, 
Sun's Apogee =27 4' 'A71, 
's eccentricit) = 0-01833. 



Antares=188W neorU 
The new moon near Ant are*, 
happene.d about G hrs. before, i.e., 
at 11 8 A.M. Kuruksetra mean- 
time and conjunction took place 
very near to the star Antares. 
which is the junction star of the naksatra Jyestha, This new 
n oon is mentioned in the Mahabharata reference (/') cited before- 

(2) We have next on Nov. 3, -2449 B.C. at G.M.N. , or 
Kuruksetra mean time 5-8 P.M. 



Mooii-1914G', 



Mean Longitude of 



Mean Sun = 20214'33", 

,, Moon = 225'40", 

Lunar Perigee =1 89 53'39", 

A. Node =12028'36". 



/. Apparent Sun=202 c 4 / 
,, Moon= 334' 

Mean longitude of Krttika 
or Ale yone = 35830' nearly. 



The conjunction of the moon with the Krttikcis had happened 
about 10 hrs. before, i.e., about 7-8 A.M. Kuruksetra mean- 
time This phase of the moon is mentioned in^Jt 
reference (it) quoted before. At 
6 below the Krttikus, . 

3-1408B ^ --^^^ 

* f O 




18 



ANCIENT INDIAN CHRONOLOGY 



(3) THE BATTLE BEGAN from Nov. 4, 2449 B.C. or the day 
following. The mean longitude of Rohim junction star or 
A Ideharan was 8 17'; the conjunction of the moon with RoJiml 
had taken place on the preceding night at about 2-30 A.M. 
Kuruksetra mean time, 

(4) On Nov. 18 at G.M.T. hr. or 5 8 A.M. Kumksetra 
mean time. 



Mean Sun=218B2' 4*. 
,, Moon = 19339' 8", 
L. Perigee = 19130'34", 
A. Node = 10142'32". 



Apparent Sun = 21658' 
Moon = 19225> 
Moon's celestial 

latitude = 58'42"N. 



Hence in the morning of Nov. 18,2449 B.C., the sunrise 
happened at 6-23 A.M. of Kuruksetra meantime and the moon 
rose at 4 29 A.M. of K.M.T. 

Thus the moon which was crescent rose about 1 hr. 54 inin. 
before the sunrise. This moonrise is spoken of in the 
bharata references (m), (it?) and (0) quoted before. 

(5) On Nov. 21, at G. M. N., or K. M. T., 5-8 P.M. 



Mean Sun = 21959' 3", 
Moon=23946'll", 
Lunar Perigee = 191 53'57'/, 
A, Node = 10131'25" 



Appt. 

,, Moon=24447'. 
Mean long, of Sravand (Altair) 
=24017' nearly. 



ON THIS DAY THE BATTLE ENDED, and the nioon had been 
conjoined with the * junction star* Sravana about 8i hrs. before, 
This was the day of the first visibility of the crescent after the 
preceding new-moon. For on the preceding day, the 20tb Nov., 
2449 B.C. at G. M. Noon, 

Appt. Sun=21927' f 

Moon =230 5', 

A. Node 10135'. 

Moon's celestial latitudes 4 1'28"N nearly. 
Moon - Sun = 1038' only. 

Hence the moon was not visible at nightfall on this day, 



DATE OF THE BHARATA BATTLE 1<J 

The month of lunar Pausa was most probibly reckoned from 
this 20th Nov., 2449 B.C. by the calendar authorities of the 
Pamlava time. 

(6) Lastly on Jan. 10, 2448 B.C. at G.M.N. or K.M.T., 
5-8 P.M., 

Mean Sun =269 16' 0", Appt. 

,, Moon = 17552'. 
Lunar Perigee = 197 28'iO" 
A. Node= 9852'33". 

Thus the sun had reached the winter solstice about 28 hours 
before, i.e., on the preceding day as already explained. The 
moon came to her last quarter in about 104 hrs. later. Bhisma 
expired on this day at about the time for which the longitudes 
have been calculated. The date of the Bharata battle is thus 
astronomically established as the year 2449 B.C. which is 
supported by the Vrddha-Garga Tradition recorded by 
Varaharnihira. 

Arc the Mahtibhurata References Later Intcipolaiionts?' 1 

The striking consistency of the Mahabharata references, may 
lead some critics of our finding to propound the the?ry that there 
were all later additions by the epic compiler of about 400 B.C., 
made with the help of an astronomical assistant of his time. 
We are, however, of opinion that such a hypothebib as to their 
origin is not justifiable. 

Fjrstly, these astronomical references are not all collected at 
any single place : they are scattered over the battle books from 
the Udyoya to Anusasana. 

Secondly, the knowledge of astronomy, developed in India 
from the earliest times up to 400 B.C., could not enable a,ny 

* Pruf . Dr M. N. Saha in his paper in " Science and Culture " for March, 1939 
pp. 488-488, raised tl.is question. The author of the present *ork replied to this 
in the " Science and Culture/ 1 July, 1938 in pp. 26-20. 



20 ANCIENT JNDJAN CliKoNULOOY 

astronomical assistant to determine the set of those astro- 
nomical references which we have used in this chapter. So 
far as our studies go, neither the astronomy of the Brahmanas, nor 
of the Veddngas, nor of the Paitdmaha Siddhdnta as summarised 
in the Paficasiddhdntika of Varahamihira, vtas equal to the 
task. The arguments in favour of our position are set forth 
below as briefly as possible. 

From the Mahdbhdrata references cited above, we have 
evolved two astronomical data for the determination of the year 
of the Bharata battle : (?) that tie year of the battle was similar 
to the year 1929-30 A.D. of our times in so far as the moon's 
phases near to the fixed stars are concerned, and (it) that the 
observers of the sun appointed by the Pandavas were satisfied 
that the sun's northerly course had begun exactly after a lapse 
of 50 nights from the evening on which the battle ended 

Before the battle broke out there was a new- moon near the 
star Antares, from which the lunar month of Agrahdyana began 
in the year. Thirteen days later in the evening, the moon 
nearly full, was observed near the star group Krttikds or Pleiades. 
The battle began from the next morning. On the night follow- 
ing the fourteenth day of the battle, a crescent moon rose some- 
time before the day-break. OQ the 18th or the last da^ of the 
battle, the moon was conjoined with Sravanci or Altair. Exactly 
fifty nights after the battle ended, Yudhistbira was satisfied that 
the sun had turned north or that the sun had readied the winter 
soUtice one day earlitr. 

As regards the repetitions of the moon's phases near to the 
fixed stars they orcur at intervals of 19 or 160 and 1939 sidereal 
years. Hence by the mere repetition of these phases of the 
moon near to the fixed stars, no date of any past event can be 
determined. Conpled with these repetitions of the lunar phases, 
we must exactly know where the winter solstice day stood in 
relation to these phases or the lunar months of the year in which 
the event happened. Here as shown before, the interval from 
January 1 to February 20 of 1930, is exactly 50 days, 

We now proceed to show that the interval of 50 days between 

the end of the battle and the first day of the sun's northerly 

: course of the year, could not be predicted by the astronomical 



l)ATJbl 01<* THE BHAUATA 11 A TILE 21 

knowledge that developed in India from the earliest times up to 
400 B.C. In Vedic times, for starting the five yearly luni-solar 
cycle or lustrum, a peculiar synodic month of Mdgha was used 
from about 30'JO B C, This lunar Magha had these three impor- 
tant features (i) that it should have for its beginning the new- 
moon at Dhanislhd (Delphinis}, (ii) its full-moon at the star 
Magha (Regulus) and (Hi) its last quarter at the star Jyesthd 
(Antares). 1 In spite of these well pronounced characters, it 
could not be a sid^really fixed lunar month. In our times such 
a month of Mdgha happened truly, according to our estimate, 
in the years 1924, 1927, 1932 and 1935 A.D. The beginning 
of this standard Mdgha oscillates between the 2nd and 6th of 
February, and its end between the 3rd and 7th of March. 
According to Varahamihira such a Mdgha came in the year 2 
of 8aka elapsed or 80 A.D., and this j ear was similar to 1924 
A.D, of our time. If we allow a slightly greater latitude, the 
year 1929 bad also this type of J\I<lghu from the 9th of February 
to the llth of M^rch. Hence both the years 1924 A.D. and 
1929 A,D. were suitable for fttarting the Vedic five-) early cycle, 
the former being more suitable than the latter. 

Now 1,)24 A.D., had the same lunar phases as 2454 B.C., 
and 1929 A. D., the same as the year 2449 B.C. This latter 
year has become the year of the Bharata battle according to our 
finding. Between the years 1921 A.D. and 1929 A.D., we had 
a Vedic luni-solar cycle of 5 years, and a similar lustrum existed 
between 2454 B.C. and 2449 B.C. Here the battle year was 
similar to 1929 A.D., as has been shown already, and the year 
exactly preceding the battle year by one lustrum was similar to 

1924 A.D. 

(1) First, let us suppose that the full^moon day of Mdgha 
and the winter solstice day were the same day in the year similar 
to 1921 A.D., exactly one lustrum before the battle year which 
was similar to 1929 A.D/ Hence the five-yearly Vedic cycle 

1 Tis topic lun been fully discussed in Chapter XIII on ' Solstice days in 

\>iJic Literature/ 

2 The reference is IHTO to the ago when Pleiade* and Reyulu* were, respectively 
near to the uu mil equinox am! the summer soldtire, i c., about 2150 B C. 



2-' ANCIENT INDIAN CHRONOLOGY 

started therefrom would end on the full- moon day of May ha of 
the battle year. It would then be usual to start the Vedic lustrum 
anew from the day following the full-moon day of Magha 
of the battle year, and this full-moon day would be taken 
for the winter solstice day according to the reckoning used. 
Now one Vedic year consisted of 12 lunations plus 12 nights ; 
hence the estimated day of the next winter solstice would be the 
27th day of lunar Magha to come. The 28th day of this Magha 
would be the first day of the sun's northerly course. This day 
would correspond with the 27th February of 1930 A..D. of our 
time. Hence the predicted first day of the sun's northerly course, 
and the last day of the battle which corresponded with January 1 , 
1930 A.D., would have between them an interval of 57 days and 
not 50 days as found by observation. Thus the predicted day of 
winter solstice could not generally agree with the accurately 
observed winter solstice day in the Pandava times. This is also 
illustrated from the following verse of the Mahdbharata, which 
contains Krsna's prediction of the first day of the sun's northerly 
course on which Bhlsma was to expire. 

tc O chief of Kurus, there still remain 56 days more of your 
life : then laying aside this body you will attain those blissful 
worlds which are the fitting rewards of your good deeds in this 
world/ 11 

This verse of the original saga is found displaced from its 
proper setting in the present recensions of the Mahdbharata. 
Krsna must have addressed these words to Bhlsma at the conclusion 
of the fight or on the day following. We shall discuss this stanza 
more fully in the next chapter. 

(2) Secondly, let us suppose that 5 years before the beginning 
of the battle year, it was found by observation that the day of the 
new-moon of Magha begun, was the winter solstice day 2 ; then at 



fipimt 



M.Bh., 8&n1i, 51, 44. 
2 Reference is here to the time about 1400 B.C., the dale of the Vedahgas. 



DATE OF THE BHiRATA BATTLE 23 

the end or termination of the five-yeaily cycle at the starting of the 
battle year, the new moon day of Magha begun, would be reckoned 
as the winter solstice day. The estimated winter bolstice day for 
the beginning of the next year would be the 12th tithi of 
the coming Magha and the first day of the sun's northerly course 
would be the 13th tithi of Magha and in our gauge year 1929-30 
A.D., it would correspond with the llth February, 1930. Between 
the ending day of the battle (corresponding with Januarj ], 1930) 
and the first day of the sun's northerly course, there would 
intervene H days as predicted and not 50 days as observed. 

Thus judging by the methods of reckoning of the Vedic and 
post-Vedic followers of the five-yearly luni-solar cycles, it was not 
possible for an Indian astronomical assistant by any back calcula- 
tion to furnish the Mahdbhdrata compiler of 400 B.C. with the set 
of astronomical references which we have used to establish that 
the Bharata battle was fought in 2449 B.C. 

Lastly, it may be contended that "the Mahublulrata writer of 
the 4th century B.(>., while inserting the astronomical references 
merely calculated back on the assumption that the Great War was 
fought when Pleiades formed the vernal equinoxial point, because 
this was an older tradition." 

We can here explore the possibilities of the above assumption 
in the following way: The year of the Brahmanas and the 
Vedtlngas consisted of 806 days and a quarter-year was thus of 
9V day?. Tfthe Krtliknx or Pleiades were at the vernal equi- 
nox, then a full -moon at the Krttikas would be on the day of 
autumnal equinox, and the winter solstice day should couie after 
9i'5 days according to this mode of reckoning. Now in order to 
interpret the Mahilbhdratti astronomical references we take a 
gauge year in which the full-moon of Kfirttika took place very near 
to the K rt tibia ; ibis- >car would be 3934-35 A.D. The day of 
full-wo<m of KurtHkn w nld correspond with 21st November, 1934. 
The predicted day of winter solstice would correspond with the 
81st of February. According to the Mahabharafa references, the 
anniversary of the last day of the Bharata battle would be Janu- 
ary 6, 1935 and of the winter solstice day the date would be the 
85th February, 7?/3fl. There would thus be a clear difference 
o/ 4 days Mwctm the estimated winter solstice day and the 



24 ANCIKST INDIAN CHRONOLOGY 

Mahdbharata-stated icinter solstice day. 1 Here if we take the 
Mahdbharata date for winter solstice to be correct, we get a total 
precession of the solstice-day amounting to 65 days, representing a 
lapse of 4810 years till 1935 A. D., and the date of the battle is 
pushed up to 2876 B.C., nearly, which gets no anchorage at 
either of the Sryabhata or the Vrddha-Garga tradition. Hence 
the above hypothesis cannot explain the possible finding of the 
Mahdbharata references as used in this chapter, by the epic 
compiler or his astronomical assistant of 400 B.C. 

It is thus established that the Mahdbharata references used by 
us for finding the date of the Bharata battle, cannot be taken as 
interpolation by the epic compiler of about 400 B.C. They were, 
in my opinion, the integral parts of the Pandava saga which 
formed the nucleus for the older Mahdbharata and the Bharata 
and were finally included in the great epic when it was first 
formed about 400 B.C. These references have, therefore, been 
taken as really observed astronomical events or phenomena, made 
hi the battle year itself and which were incorporated in the 
original Pandava saga. 

CONCLUSION 

We have thus come to the most definite conclusion that the 
Bharata battle did actually take place in, -2526 of Saka era or 
ki449 B.C. For one single event only one date is possible. We 
tiust, the problem of finding this date from the Mahdbharata 
data, has been satisfactorily solved in this work for the first time. 
The date arrived at makes the event as contemporary with the 
Indus valley civilization. In the MahdbMrata f we get many 
references to show that Rdksasas, Asuras and the Ar)an 
Hindus had their Kingdoms side by side. In Vana-parva or 
Book III, chapters 13-22 give us a description of the destruction 
of Saubha Purl by Ersna. This may mean the destruction of a 
city like Mahenjo Daro. The Bharata battle was a pre-historic 
event and the Puranic dynastic lists relating to this period 

1 By the mean reckoning the number of days from the full-moon day of Rarttfta 
to the 7th day of the dark half of M&gha x 29*6 x 34-7 = 95*5 days and 95*5 da. -91*6 
da. is also = 4 days. 



DATE OF THE BH1EATA BATTLE 25 

cannot be taken as correct. They are mere conjectures and could 
be accepted only when they could be verified from other more 
reliable sources. There are undoubtedly several gaps in these 
lists, which have yet to be accounted for. In many cases, wrong 
traditions may be found repeated in many books ; they all may 
be echoes of one statement ani are not acceptable. 1 Not such 
are the Mahdbharata references which we have collected from the 
Udyoga to the AnuSasana parva. We trust, my thesis stands 
on solid astronomical basis selected with the greatest care and 
discrimination. The misinterpretations of the commentator have 
been, on some occasions, confounding for a time. 

The historical methods are often liable to very serious errors 
by wrong identification of persons from a similarity of names. 
The astronomer Parasara, probably a man of the first and second 
centuries of the Christian era, was wrongly identified with 
Parasara, the father of Vyasa, the common ancestor of the 
Kauravas and the Pandavas, by the earliest researchers, Sir 
Wm. Jones, Wilford, Davis aud Pratt. 2 They based their calcula- 
tion on the statement of this Parasara, the astronomer, as to 
the position of the solstices ; their calculation has but given an 
approximate date of an astronomical event, but neither the time 
of the Pandavas nor of the astronomer Parasara. Such mistakes 
have been made by many subsequent researchers, who have used 
the sameness or similarity of names as a basis for a historical 
conclusion. Not such are the astronomical references used in 
this paper. They are all definite in meaning and, as we have 
said already, for an event of which the date is not recorded in a 
reliable historical work, no better evidence of date is possible. 
Our examination in the light of these references fully corroborates 
the date recorded by Varahamihira whose statement must now 
be regarded as more reliable than those of the host of the writers 
of the Purdnas of unknown name and time. 



l For a full discussion of Paranic evidences the reader is referred to Chapter HI. 
* Asiatic Researches, Vol II, etc., of. also JASB, for 1862 A.D., p. 51. 

Also Brennand's Hindu Aatronomj, Oh. IX, pp. 112-135. 

4 1408B 



26 ANCIENT INDIAN CHRONOLOGY 

A note on the selection of astronomical references 

from the Mahdbhdrata 

for 

The Date of the Bharata-Battle 

In our selection of astronomical data in the present chapter 
no use has been made of those that are found in chapter 143 of 
the Udyogaparva and in chapter 3 of the Bhismaparva. 1 
I have understood them to be mere astrological effusions of bad 
omens ; they are also inconsistent in themselves, and as such 
they cannot have any bearing as to the date of Bharata-battle, 
These are : 

ft 



Udyogaparva, 143. 

" The planet Saturn which is acute (tlkma) and of great 
effulgence oppresses the star (Rohim or Aldebaran) of which 
the presiding deity is Prajapati, and causes great affliction to 
living beings, slayer of Madhu (Krsria), Mars having taken 
retrograde motion near to Jyesthti (or Antares) has now 
approached the star-group Anuradha, ('junction star' 8 Scorpionis) 
or has already reached it of which the presiding deity is Mitra. 
More specially, O descendant of Vrsni, a planet troubles the star 
Citrd (oc Virginia). The marks on the moon are changed and the 
node (Rdhu) is reaching the sun." 

Here Saturn is indicated to have been in opposition ; Satnrn 
being near Rohinl, the sun must be near to the star Jyesthd 
(Antares). Again Mars is spoken of as in the naksatra Anuradha 

1 See Appendix (Vj to <f An Indian Ephimeris, A.D. 700 to A.D. 1709 by Diwan 
Bahactur &. P. Swamikannu Pillai, I.S.O., pp. 479.83. 



DATE OF THE BHlIUTA BATTLE 27 

and is retrograde ; hence the sun must be nearly opposite to it 
and ne&r to the star group Krttikds (Pleiades). The inconsistency 
of the statements is apparent. A planet which is not named 
is spoken of as have neared to <x Virginis. All this is mere astro- 
logical effusion stating evil omens, and cannot have any chrono- 
logical bearing. We next turn to another similar statement in 
the Bhtsmaparva, chapter 3. 



^br fefen 



" The white planet (Venus) stands by passing over the star 
Citra (<x Virginis). A dreadful comet is stationed at the star 
group Pusya. Mars- retrograde is' in the Maghas, and Jupiter 
iuSravana division. The son of Sun (Saturn) oppresses the 
naksatra Bhaga (P. Phdgml) by overtaking it. Venus in 
the 'naks atra Proslhapada (P. Bhddrapada) shines there. Both 
the sun and moon oppress the star or naksatra RohinL A 
cruel planet is stationed at the junction of the Citra and Svati 
naksatras. The ruddy planet (Mars) looking like fire having got 
the even motion at 3 warp stands by overpowering the naksatra 
Brahma, Stationed near the VifakMs, both Jupiter and 
Saturn are seen burning as it were and would continue so 

for one year." 

We tabulate below the positions of the planets in the two 

references : 



28 



ANCIENT INDIAN CHEONOLOGY 



Planet 


Position in Nakatra 
in Ref. I 


Position in N\ ksatra 
in Eef. II * 




Saturn 


Robin! 


P. Phalgnnl 
or Vigakbas 




Mars 


Anuradha 


Magba or Robini 




Sun 
Moon 


Jyestba or Krfctika 


Robini or Dhani^ba 
Bobini 


(i.e., opposite to 
Magba) 


Unnamed Planet 


Citra 


Bet. Citra & Svati 




A-Node 
Venus 
Jupiter 


Near to Jyestha 

... 


P. Bhadrapada 
or Citra 

Sravanaor ViSakba 





All this is hopelessly inconsistent astrological effusions of 
evil omens fit for Mother Groase's Tales only. Still something 
of chronology of the Bharata battle was attempted by late Mr. 
Lele from them for which the reader in referred 'to Dlksita's 
W*cfta s^tl^rra, pp. 119-20 (Istedn.); the date arrived at by 
him was 2127 years before 3102 B.C. a most fantastic result ! 
His finding of the positions of planets does not also agree with 
the abovemenfcioned positions indicated in the Mahdbhdrata 
as explained already. 

We again have the two statements : 



M.Bh.,Sabha 9 Ch. 79. 

\n*\\ 

M.Bh., 3alya, Ch. 59. 



i.e., " Eahu (also) eclipsed the sun, king, when it was not a 
new-moon/' 

These statements are also mere poetic effusions. In BJusma 
parva, Chapter III, we have another statement which says : 



e< Ihe moon and the sun were eclipsed in one month on the 
13th day of either half/ 1 - 



DATE OF THE BHABATA BATTLE 



29 



We cannot put any faith in any statement of this chapter 
of the Mahdbharata. Two eclipses, one of the moon followed 
by the other of the sun in a fortnight, are not of very rare occur- 
rence. In the year 2451 B.C. two such occurred: 

(1) On Aug. 30, 2451 B.C. at 18 hrs. Q.M.T., or Kuruksetra 
mean time 23 hrs. 8 min. 



Hence there was a lunar eclipse 
on this day visible at Kuruksetra, 
and ifc was of no small magni- 
tude. 



Mean Sun=137 54' 5F-56, 

,, Moon = 31 7 k8'47"-99, 
Lunar Perigee=101 13' 3o"-60, 

A-Node=144 e 37' 5"-51, 
Sun's Apogee = 27 1' 52" 

, , eccentricity = -018331 

Again on Sept. 14, 2451 B.C. at G.M.T. hr. or 5-8 A.M. 
Kuruksetra Mean Time : 



Mean Sun = 151 57' 35"-28, 

,, Moon = 145 14' 37"-54, 
Lunar Perigee =102 48' 50"-69, 



A-Node-143 



48"-96. 



This solar eclipse is discussed 
in a subsequent chapter. It was 
visible in the morning from 
Kuruksetra. 



Now on Aug. 16, 2451 B.C. at G.M.T. hr. or KM. time 
5-8 A.M. 



Mean Sun= 123 22' 33"-69, 
Moon = 123 7'41".32, 
L-Perigee=99 35' 0"-08, 
= 14523'57"-36. 



N.M. happened about 8 hours 
before. 



Hence the N.M. happened on Aug. 15, at K.M. time 21-8 
nearly. -The moon was not visible on the 16th. The days of 
the month were reckoned from 17th or 18th Aug. 2451 B.C., 
the lunar eclipse fell on Aug. 30 and the solar eclipse on Sept. 14, 
2451 B.C. The eclipses in question happened two years before 



30 ANCIENT INDIAN OH110NOLOOY 

the date of the Rharata battle as ascertained in this chapter, 
viz., 2449 B.C. 1 

U t e 2.Ca)npamon of the Mahabharatu slatfinents of 
Planetary positions with those calculated /or t>19 H.C., I lie. ycur 
of the Bharata battle. 

In this connection we think it necessary to examine' all the 
MaMWidrata statements of planetary positions at the different 
times of the year of the Bharata battle, and compare them with 
the planetary positions in 2449 B.C. on the following dates:- 
(a) October 14, 2449 B.C., on the morning of which Krsnu m't 
Karna as described in the Udyotja-parDa, chaptera 14*J and 14.'i 
as quoted already on page 26 ; (b) November ;J, '2449 B.C f /.r., 
on the evening preceding the first day of the buttle for which tltt* 
planetary positions are stated in chapters 2 and 3 of tin* 
Bhtsma-parva of which those in chapter '< have been quoted *m 
page 27; and (c) November 21, sM4H H.C. fur whieh the 
planetary positions are found in chapter 9-1 of t!ie KtinnhinirK<i> 
We now quote below one stanza from the /J/u>y;m////Tr/, 
2, stating the position of Saturn, thus: 



" king, Saturn (the slow-going planet) Maud* 
the star Eohinl (Aldcbaran) the rnoon'B markn aro reverM*d 
dangers are imminent." 

Again in the Karna-parva, \ve have 



, 0>I, 40 and 5 

1 In pages 482-83 of his work <m " Indian ^phenmrin/' Iiw*n 
L, D. SwamikfiriiDU Pillai, I. 8. (), lends *ome iupporUto tli ulu^i* findihg of ifc* 
dato of the Bharata battle Mm. Sudhikara Dviv(ii tUuei'e|tt Umi ih 
battle was fought and the reign of Yudlii^hira begun in 0449 B.C-, r*d hi4 
of the Mahd'Siddhanta, Contents, pp, 1*8, 



DATE OF THE BHIEATA BATTLE 31 

" When Karna was killed the streamlets ceased to flow and 
the sun set. The white planet (Venus) became of the colour of 
fire and Sun (combust or heliacally set?) and the son of Moon 
(i e., Mercury) became heliac&lly visible obliquely." 

"Jupiter surrounding the star Roliinl (Aldebaran) became 
as bright as the sun and the moon." 

The planetary positions according to our calculations are 
exhibited below : - 



Planet 


October 14, 6 A.M. 
K. M. T. 


Nov. 3, G. M. N or Nov. 21, C A.M. 
K. M. T., 17hrs. 8 mins. K. M. T, 


Longitudes 
of Planets. 


Ref. stars 
with longs. 


Longitudes 
of Planet 2 . 


Kef. stars 
with longs. 


Longitudes 
of Planets 


Ref. stars 
with longs. 


Sun 
Moon 


181 10' 
85 22' 


8 Scorpii 
181 4' 

a Leonis 
88 20' 


202 4' 
3 34' 


A. Scorpii 
203 5' 

a Tauri 
8 17' 


219 59' 
237 50' 


ff Sagitler 
2-20 '53' 

a Aquila 
240 16 


Mercury 


199 45' 


A. Scorpii 
203 5' 


215 14' 


S Sagitter 
213 5' 


190 9 22' 


\ Scorpii 
203 5' 


Venus 
Mar3 


176 T 
144 4' 


5 Scorpii 
181 2' 

a Virginia 
142 18' 


200 56' 
157 45' 


X Scorpii 
203 5' 

a Libra 
163 35' 


223 52' 
169 33' 


<r Sagitter 
2*20 53' 

i Libra 
169 30' 


Jupiter 


11 25' 


a Tauri 
8 17' 


8 36 


a Tauri 
8 17' 


7 50' 


a Tauri 
8 17' 


Saturn 


357 59' 


7? Tauri 
358 30' 




356 27' 


1? Tauri 
358 30' 


355 24' 


ft Tauri 
358 30' 

i 



As to Saturn, it is found twice stated that it was oppressing 
the star Roliinl (Aldebaran) of which the presiding deity is 
Brahma, the Creator or Lord of men. But the planet stands at a 
distance of about 10 from Aldebaran. The distance for the aspect 
of " oppression " is perhaps acceptable. As to Jupiter it was 
throughout retrograde and stood near to the star Aldebaran. Mare's 
progress extends from the star Citrd (a Virginis) to that of Visakha 
(i Libra). The planet is called "parusa" or cruel in chapter 3 
of the Bhlsma-parva and in Chapter 142 of the Udyoga-parva 
where it is spoken of as "oppressing" the star Citra or 



82 ANCIENT INDIAN CHRONOLOGY 

a Virginia, but is not given any name. Venus stands throughout 
in the position of " Combust" or heliacal setting. Mercury 
was visible a little before the sunrise on Nov. 21, morning. On 
Nov. 8, at evening the moon is oppressing the stars Rohinl, 
while the sun standing at 202 4' may be taken to " oppress " 
another Rohinl which was Antares called also Jyestha of which 
the longitude was 188 16' nearly. It seems that in the Udyoga, 
143, the verses 8 and 1'J speak the truth : and in BJilsma, 2, the 
stanza 32, and in Bhlsma, 3, the stanza 17 alone, tell the correct 
positions. In the Karna-parva, 94, the verses quoted are 
verified by our calculations. The Mahdbharata statements of 
planetary positions are thus found to be full of ' truths and 
fiction " and I trust, in our selection of data for the year of the 
Bbarata battle, we have been able to avoid " fiction " and to 
accept the true astronomical events on which our finding of the 
year as 2449 B.C., has been based. 

The last but not the least important astronomical indication 
is that Yudhisthira was consecrated for the Afoamedha sacrifice 
which was year-long and used to be begun with the beginning 
of spring ( astronomical, when the Sun's longitude became 
330). The date in question is stated to be Citrdpurnamasa 
) or the day of the full-moon near the star 



a Virginis or Citrd. Consistently with our finding the year 
of the Bhcmita battle as 2449 B.C., the date for Yudhisthira's 
consecration for the A&vamedha sacrifice becomes 

March 11, 2446 B.C., on which at G. M. N. or K. M. T. 
17 hrs. 8 mins. 



True Sun = 329 42' 27" 

Moon = 144 35' nearly 
a Virgini* = 142 23' 



Astronomical spring begins in 
about 7 hrs. and F. M. in about 
10 hrs. 



This was the day of the full-moon which is spoken of in the 
Afaamcdhaparva, Ch. 72, thus: 



" Your consecration will be on the day of the full-moon at 
Qitm (a Virginia) , 



DATE OF THE BHARATA BATTLE .|l 

The beginning of the five-yearly luni-solar cycles or yug,u of 
the Veddngas is associated with the day of the winter solstice 
thus : 

'When the sun, the moon and the ntiksitra Dlwnixthl 
(Delphinis) ascend the heavens together, it is the beginning of 
the Yuga (cycle), of the month of Maglia or Tapas, of the 
light half and of the sun's .northerly course.' 1 

Again all Hindu calendars and the Puranas* say that the 
Kaliyuga began with full-moon day of Mfiyha. This Ktilt- 
beginning was quite different from the astronomical Kuli epoch, 
the later started from the light-half of Caitra, i.e., from Feb. 
17-18, 3102 B.C. Judging by the beginning of the luni-solar 
cycles of the Vedanga period, we should identity the day of the 
winter solstice with the full-moon day of Mdfjlia, in finding 
the beginning of the Kaliyuga which is mentioned in the 
MaMbMrata and the Puranas. 

Now we assume that the Puranic Kaliyuga was started from 
the full-moon day of the standard month oj Magha, of which 
we have spoken before, 3 and that day was also the day of the 
winter solstice. We also understand that it is the same Kali 
yuga, of which the reference is found in the ^ahabli'iratd and 
the Puranas. 

We agree to accept that this standard month of Magha 
happened in our own time in 1924 A.D. from the 5th of February 
to the 5th of March, with the characteristics, viz., that it began 



also 



3 rd Chapter I, page 21. 
a 1408B 



42 ANCIENT INDIAN CHRONOLOGY 

with the New-moon at the beginning of the Dlianistha cluster, 
had its Full-moon near the MagMs and the Last Quarter 
conjoined with Jyestha or Antares. 

Now according to our finding the year of Bbarata battle was 
2449 B.C. and in so far as the moon's phases near to the fixed 
stars are concerned it was similar to 1929 A.D, 1 Hence 2454 
B.C. was in the same way similar to 1924 A.D, 

It was in 2454 B.C., on the 9th January, that a full-moon 
happened. At Greenwich mean noon or 5-8 p.m. Kuruksetra 
time on that date the apparent longitudes were for 

Sun =269 36', 
Moon=86 1&, nearly. 

The moon was ahead of the sun by 176 40' nearly ; and the 
fall-moon happened in about 7i hours at about 1 15' ahead of 
the star Regulus or Maglia. The sun reached the winter solstice 
2| hours later. The day of the winter solstice and the full-moon 
day were the same day according to MahdbMrata convention * 
of its ending with the sunrise. 

Most likely the Mahabharata Kaliyuga truly began from this 
year of 2454 B.C., lOfch January, when the Pandavas were still 
on exile. The year of the Bharata battle or 2449 B.C. marked 
the end of five-yearly cycle, was within the sandhi or junction 
of the Dvdpara and Kali ages. This smdhi was a period which 
was taken to last a hundred years, f.e,, till about 2354 B.C. 
most likely. During this period men were uncertain when the 
Kaliyuga began. Hence the year of Bharata battle coming five 
years after 2454 B.C. was itself taken as the beginning of the Kali- 
yuga. The year of Krsna's expiry coming 36 years 3 after the 
great battle and 41 years (=38+3) after 2454 B.C. was also a 
beginning of the Kaliyuga* In these years also the day of the 
winter solstice was not much removed from the full-moon day 

1 The foregoing chapter, pi 12 et $eq. 
* M Bh. t Atvamedha, 44,2, 



M , Bh.> Mausala, Ch. 1. 

rt 



Visnu Pmrana, IV, 24, 11Q, 



DATE OP THE BHARATA BATTLE 48 

of Mdgha. Hence followed a ' rule of the thumb ' that in this 
period, whenever the standard month of Magha should apparently 
return, the day of the f ull-inoon was taken as the ^winter solstice 
day. 

As an illustration of how the above ' rule of the thumb ' 
was followed for predicting the winter solstice day in Pandava 
time, we have already considered the words of Krsna as to the 
expected day of Bhfsrna's expiry in -Chapter I. 1 We propose to 
discuss it again by back calculation. 

It has been shown that the observed day of winter solstice 
must have been the same as the MdgJia full-moon day of 9th 
to 10th January, 2454 B.C. After the completion of the five 
yearly luni-eolar cycle in 2449 B.C., there was apparently a 
return of the standard month of Mdgha. The full-moon fell on 
the 14th January, 2449 B.C. on which at G-.M. noon: 

Appt. Sun = 274 53' 

,, Moon=90 89' Dearly. 

Thus the fall-moon happened about 8| hrs. later* This 14th 
of January was the estimated day of the winter solstice for the 
year 2449 B.C., but it could not be the accurately determined 
solstice day. Now the Vedic year was of 366 days or 12 luna- 
tions plus 12 nights. If we count 366 days from January 14, 
2449 B.C., we arrive at the estimated day of the winter solstice 
as January 14, 2448 B.C. The first day of the sun's northerly 
course (as estimated) would be January 15, 2448 B.C., as the 
day for- Bhisma's expiry. Now the battle ended on the 21st 
November, 2449 B.C. The number of days between these dates 
becomes 55 days. But one day more was probably included in 
this period in the following way : 

We have shown in Chapter I, that in the yeai 2449 BC,, 
the calendar authorities of the Pandava time, most probably began 
the reckoning of the lunar month of Pansa from the 20th of 
November. 2 Hence between this date and the expected day of 
Bhisma's expiry, the 28th day of lunar Magha to come, there 
would be 29*5 +28=57'5 days (here the estimated day of winter 

l M. Bh., Santi, 61, 44, he. cit> 
9 Chapter I, p. 19. 



44 ANCIENT INDIAN CHEONOLOG^ 

solstice was the 27th day of lunar Magba and Bhfsrna was to 
expire on the following day). Now reckoning from the day on 
which the battle ended till this expected day of the sun's norther- 
ly course there would be 56 or 57 days. This would explain 
Krsna's prediction about the expiry of Bhisma, most probably 
made on the date on which the battle ended or on the day 
following. 

(e) Evidence of the MaliSbMrata Kali-reckoning 

A question may now be asked if there is any evidence that 
this Mahdbhdrata jfiTaK-reckoning was current in India for some 
time. The following instances may be cited : 

(1) A versa quoted in a work named the Laghu Bhdgavat- 
dmrta ,by Rupa Gosvami, thus speaks of the time when the 
Buddha was accepted as an incarnation of Visnu * : 

* He was revealed when 2,000 years of tbe Kaliyuga had 
elapsed ; his form was of a brown colour, two-handed and bald- 
headed/ 

Now the Buddha's Nirvana took place according to the latest 
authorities at his age of eighty in 483 B.C. 2 He was thus born 
in 563 B.C., and began preaching the truth that came to him 
when he was thirty-five or about 528 B.C. Two thousand years 
before the Nirvana year was the date 2483 B.C., and our finding 
of the year of the battle is 2449 B.C. Hence according to the 
rough statement quoted above a Jffl/z-reckoning was started near 
about the year of the battle. 

(2)" Again all orthodox Bengali almanacs record that * in 
the Kali age, kings Yudhisthira, Parlksit, Janamejaya, Satanlka, 
Vikramaditya and others of the lunar race, 120 in number, ruled 
for 3,695 years 3 months and 18 days till the Muhamroadan 
conquest (of Bengal presumably, as it is essentially a Bengal 
tradition). The Sena dynasty of Bengal, which claimed its descent 



Quoted by Sir William Jones in his paper in the Asiatic Researches, Vol. II, p. SJ2. 
2 Perhaps the real Nirvana year was 544 B.C. 

3 



..,* etc. 



I) ATE OF THE BHIRATA BATTLE 45 

from the lunar race, reigned independently in East Bengal for 
some years even after the conquest of West Bengal by Muham- 
mad Ibn Bakhtiyar. If we count 3,695 years from 2449 B.C. 
we arrive at the year 1247 AD. for the extinction of ihe Sena 
dynasty, and is very nearly true historically. Hence the 
Mahdbhdrata jEMi-reckoning was started from the zero year of 
the Tudhisthira Era, the very year of the Bharata battle. 

We trust, further evidences as to this Mahdbhdrata Kali- 
reckoning have all been supplanted by the astronomical Kali 
years started by iryabhata I, in 499 A.D. So great was the 
fame of 5.ryabhata I, as regards astronomy and reckoning time, 
that very few dared to contradict him. Eavikirti, the famous 
writer of the Aihole inscription of Pulakeffin II (634 A.D.), 
accepts Aryabhata's finding of the year of the Bharata battle in 
speaking of his time as 3,735 years elapsed from that event. 1 

To sum up : The Mahdbhdrata indeed says that the Bharata 
battle was fought at the junction of the Kali and Dvdpara ages ; 
but the Mahdbhdrata Kali age was different from the astronomi- 
cal Kali age started by a back calculation by Aryabhata I, in 499 
A.D. The former Kaliyuga truly began from 2454 B.C. (10th 
January). Even the year of the Bharata battle (2449 B.C.) was 
in itself a possible beginning of this Kaliyuga, starting from 
the 14th January, 2449 B.C. We have sho\vn examples of the 
Mahdbhdrata jSTaZi-reckoning that have continued up to the 
present time from some other source*. The astronomical Kali- 
reckoning is a mere astronomical fiction created by Aryabhata I, 
for a definite astronomical purpose, is an unreal thing as it was 
unconnected with any real astronomical event, is the result of a 
back calculation based on incorrect Astronomical constants. It 
never could have existed before 499 A.D. and thus cannot truly 
point out the time of any historical event prior to this date. 
Thus the iryabbata tradition that the Bharata battle was fought 
in 3102 B.C. is totally indefensible is a pure myth. 2 



EpigrapTiia Indica, VI, pp, 11-12- 

2 Cf. Dr. Fleet's discussion about this Kali era in JEAS, 1911 pp. 479 et sty., 
and pp. 676 et esq. 



CHAPTER III 

DATE OF THE BH1RATA BATTLE 

Bharata-Battle Tradition (C) 
2, Purdnic Traditions and Evidences 

Befoie we can consider the Purdnic traditions and evidences 
as to the time of Bbarata battle, it is necessary for us to-establish 
which of the Puranas, as we have them now, have the oldest 
strata in them and which the latest. In fact we have to settle 
which are to be believed and which not, or which were the 
originals and which the borrowers and interpreters. We have 
to think of : 

(a) The Sequence of the Puranas 

The Puranas which apparently seem to throw any light as 
to the date of Bharata battle are : 

(1) The Matsya Purana 9 

(2) The Vdyu Purana > 

(3) The Visnu Purdna 9 and 

(4) The Bhdgavata Purana. ' 

In all these Puranas we have the records of some of the earlier 
positions of the equinoxes and solstices, which are mere traditions 
and were not true for the time of composition of these works. 
The latest positions of the solstices as given in these works 
may be some guide a* to the real sequence of these Puranas. 
The Matsya Purana says that the sun reached the southernmost 
limit in Mdgha and notbernmost limit in gravana. 1 This is of 
the same type as of the Jyautisa Veddnga rule ' Mdgha-fravanayo* 

1 Matsqa Pura%a t 124, 44 and 60. 



DATE OF THE BH3JRATA BATTLE 47 

ssadd ' l and this was true for about 1400 B.Q, The same 
statement occurs also in the Vdyu Parana? together with the 
more definite statement as to the position of the Solstices, viz., 
thafc of the naksatras the first was tfravisthd.* A Liio later the 
Vdyu Parana again says that the circle of constell&tions began 
from the naksatra tSravanaf Hence the latest indication of the 
position of the winter solstice was true for about 400 B.C., and 
It is the same as in the. present recension of the Maliabharata* 
Thus from the astronomical indications it appears that the , 
Matsya Purdna has the oldest Purdnic stratum, then comes the 
Vdyu in the same respect. 

Another evidence which helps 'our finding is that both the 
Matsya and Vdyu Purdnas are mentioned and quoted in the 
present recension of the Mahdbhdrata.* According to Pargiter/ 
of the Vdyu and Matsya Purdnas, the Matsya gives the oldest 
version, Vdyu the next in so far as the dynastic lists of the Kali 
age are concerned. Hence our finding of the sequence of the 
Purdnas has some support from Pargiter and so also from Dr. 
V. A. Smith. It must be clearly understood that we do not 
mean to say that the Purdnas as a class of literature did not 
exist before the present Matsya and Vdyu Purdnas began to be 
compiled. In the Satapatha Brahmana or the Brhaddranyaka 
Upanisat? we find the enumeration of different classes of 
literature in which the Purdnas have a place. In the Asvaldyana 
Grhya-Siitra, the Purdnas and Gathd-Narasamsls 9 are distinctly 
mentioned. We do not, however, know the names of the Purdnas 
which were current in the age of the Brdhmanas or of the Sutras. 

1 Yajusa Jyautisa, 7. 



H^T H 

2 Vayu Purana, 50, 172 and 12,7. 

3 Ibid., 53, 111-116. * IbM 53, 
* M. Bh. 9 Avamedha, 44, 2 ; for discussion, c/. Chapter I, p. 1. 

6 M. Bh., Vana, 187, 55; also M. Bh. t Vana, 191, 16. 



1 



7 Pargiter's Kali Age, Introduction, p. XX. 

8 Brhaddranyaka Upanisat, IV> 5, 11. 
liialayana Grtya-Sutra, 3, 3, 1. 



48 ANCIENT INDIAN GHEONOLOGY 

Now coming to the Vimu Parana, we find that it is the 
telling of Parasara, the father of Vyasa to one Maitreya during 
the reign of Pariksit, 1 the grandson of Arjuna. Thus Vyasa 
being the grandfather of the Pandavas, Parasara was the great- 
great grandfather of Pariksit. la the Mahabhdrata itself 
Parasara is nowhere described as taking part in the events of 
the Pandava time. Hence the story of the origin of the Visnu 
Purana conflicts with our sense of historical perspective. 

Again coming to the latest position of the solstices as stated 
in the Yisnu Purana we find that it says 2 that the sun turned 
north at the first point of Mak&ra (Capricorn) and turned south 
at the first point of Karkat a (Cancer). Such a statement at a 
vital point at once should place the present recension of the Visnu 
Purana between 499 A.D. to 700 A.D. Similar remarks apply 
to the Bhagavata Purana also. 

We fchus come to the conclusion that the oldest Purdnas are 
the Matsya and Faj/u, and the Visnu and the Bhdgavata the latest 
from a consideration of the astronomical indications in them. 
So when we attempt at finding the year of the Bharata bittle 
from the Puranas, we should place the greatest reliance on the 
Matsya and then on the Vayu accounts. The Visnu and 
Bhagavata evidences should be considered as mere conjectures 
and misinterpretations of the Malsya texts and as such are least 
reliable. We now proceed on to consider the Puranic dynastic 
lists as given in the Matsya Parana. 

(b) Puranic Dynastic Lists 

The Puranic dynastic lists Apparently seem to maintain * 
continuous record from the year of the Bharata battle down to 
the extinction of the Andhras. The accounts of these lists contain 
two sorts of statements, fe., (1) in which the reign periods of the 
kings are severally stated, behind which there is apparently the 
character of real chronicling, and (2) the statements of the reign 
periods of the different dynasties made collectively, which are 



Vimu P /-ana, IV, 20, 33; 
Wd. t II, 8, 28-80. 



DATE OF THE BHiRATA BATTLE 49 

eyidently the work of later summarizers. We shall consider 
chiefly the Magadhan dynasties, the first of which was the 
Brhadratha dynasty. The Matsya account reads as follow* 1 : 

" Henceforward I will declare the Brhadrathas of Magadha 
who are Kings in Sahadeva's lineage in Jarasandha's race, 
those past, those existing and those again who will exist", I will 
declare the prominent amongst them", listen as I speak of them/ 1 

The dynastic list is thus professedly incomplete as it contains 
only the name* of chief kings and the durations of their rules, 
The narration next runs thus 2 : 

" When the Bharata battle took place and Sahadeva was slain, 
his heir Somadhi became king in G-irivraja ; he reigned 58 years. 



crar 



I n 



^(ff Ml^jfci I ft^i H 



w. H 



50 ANCIENT INDIAN CHRONOLOGY 

In his lineage Sruta&avas waa for 64 years. Ayutayus reigned 
26 years. His successor Niramitra enjoyed the earth 40 years 
and went to heaven. Suksatra obtained 56 years. Brhatkarman 
reigned 23 years. Senajit is also gone after enjoying the earth 
50 years, Srutanjaya will be for 40 years, great in strength, 
large of arm, great in mind and prowess. Vibhu will obtain 
28 years ; Suci will stand in the kingdom 58 years. King Ksema 
will enjoy the earth 28 years. Valiant Suvrata will obtain 
the kingdom 64 years, Sunetra will enjoy the earth 35 
years. And Nirvrti will enjoy this earth 58 years. Trinetra 
will next enjoy the kingdom 28 years. DnlhiHcni will 
be 48 years. Mahlnetra will be resplendent 33 years, fiwala 
will be king 32 years. King Sunetra will enjoy the kingtfom 
40 years. King Satyajit will enjoy the earth 83 years, And 
VWvajit will obtain this earth and be 25 years. Ripuiijaya will 
obtain the earth 50 years." 

Then the Purayic summarizer says J : 

" These sixteen kings are to be known as future Brhaclrathss. 
Their life-time will exceed by twenty years (the normal span of 
life) and their kingdom will last 700 years/ 1 

As we shall see, that these 16 Kings are all named in the alxnv 
lists form Senajit to Ripunjaya, and the mm total of thmr rule* 
comes up correctly to 700 years. The account is concluded by* : 



?r: \\ 
ifir*f ^ 
f^rf^wrPr 



TOWT 



9* gtn: i 
' f ? 



rl above have been rcrv r*n fully com pl !r] f r ., 
of the Kali A g ,. j n th * imwUijoa .j tfo I h*f* f|| ow- .j p wgiliff 



DATE OF THE BH1RATA BATTLE 

" These future Brhadrathas will certainly be 32 kings in all, 
and their kingdom will last fall thousand years indeed." 

The list of these Brhadratha, kings as named above may be 
made up as follows, It should be clearly borne in mind that 
there are gaps to be filled up in this list the gaps which we 
do not know how to fill up : 



1 Past ' Kings Years of 
Rule 


' Present * and * Future ' 
Kings 


Years of 
Rule 


Somadhi ... 58 


Sena jit 


... 50 


Sruta6ravas ... 64 


Srutanjaya 


... 40 


Ayutayus ... 26 


Vibhu 


... 28 


Niramitra ... 40 


Suei 


... 58 


Suksatra ... 56 


Ksema 


... 28 


Brhatkarman ... 23 


Suvrata 


... 64 


Total Years of ' Past ' Kings 267 


Sunetra I 


... 33 




Nirvrti 


... 58 




Trinetra 


... 28 




Drdhasena 


... 48 




Mahinetra 


... 38 




Sucala 


... 32 




Sunetra II 


... 40 




Satyajit 


... 83 




Ripufijaya 


... 50 




Total Years of c Present 
and ' Future ' Kings 


... 700 



In the above list there are named 22 kings in all, but nowhere 
do we find a clear statement that any one king was the SOD of 
the king named before him or he was the father of the nezt king. 
On the other hand we have the introductory statement that these 



62 ANCIENT INDIAN CHBONOLOGt 

were the chief kings of the line running from Somadhi, or that 
the list of kings is incomplete from the start to finish. The 
sixteen of the * future* Brhadrathas named in the list were only 
those of extraordinary longevity. The total number of the 
' future ' Brhadrathas is again stated definitely to be 32 and that 
the total duration of their rule would be full 1,000 years. It is 
not possible to arrive at any definite conclusion as to the duration 
of the kingship of the Brhadratbas from such an incomplete list. 
In order to understand the statements of the Purdnic summarizerfi 
we however take the incomplete list as complete and see what 
results we are led to. We have the series of dynasties as 

follows : 

Total Years 

(1) BrLadrathas of Magadha from the year of ... 967 

Bharata battle. 

(2) Pradyotas of Avanti } ... ... ... 173 

(3) Sisunugas of Magadha 2 ... ... ... 360 

Total 3 Years ... 1,500 

Then carae the accession of Mahapadma Nanda who was 
the founder of the Nanda dynasty of Magadha which lasted, 
according to the Purdnas, full 100 years* 

Thus between the year of the Bharata battle or of the birth 
of Parlksit to the accession of Mahapadma Nanda, as worked out 
from the dynastic lists of the Puranas there was the interval of 



Sftwf: (sFnr:) ^nfo* wi ^jsrofitf^ift n 

Here compare the Vifftiu statement which makeslPulika the minister of tht last 
Brhadratha Bipufijaya, 

1 Here the collective statement runs thus : 



u 

* The Steunagas who were K^atriyas of an inferior class will reign for 360 years/ 
3 According to Visntt and Bhagavata Puranas the period of Brhadrathas is 
1,000 years and that of the Pradyotas is 138 years and of the &s*uaagas 360 years, 
Thus the total corn** np to 1,498 jears. 



DATE OF THE BHARATA BATTLE 53 

1500 years nearly. This is in agreement with the following 
statement of the Purdnic summarizer : 



' From the birth of Panksit to the accession of Mahapadma 
Nanda, the interval is to be known as one thousand five hundred 

years.' 

We should here be very careful to ascertain what the second 
half of the second line of the above verse was, according to the 
Puranic summarizer. The variant readings are Cf sytf 



and 2?* irasrat^'. The very 



next stanza runs thus : 

\ 
t 

IS \\ 



The substance of which is that between Mahapadma and 
the extinction of the Andhras the time interval was 836 years. 
According to the dynastic lists the sum total of the durations 
works out as : 

Nandas ... 100 years 

Mauryas ... 

gungas ... 

Kanvas ... 45 > f 

Andhras ... ... 460 ,, 

Total 2 854 years 

Here a difference of 18 years is inexplicable as we do not 
know how long Mahapadma Nanda ruled. 

Now the interval between the birth of Parlksit and Nanda's 
accession = 1500 years as shown before, and the interval between 
Nanda's accession and the end of Andhras =854 years as shown 

1 Pargiter has traced this reading in cejMt., bMt., JnMt, blVs. recensions 
according to his notation in his Dynasties of the Kali Age, p. 58. 

2 Arvnrdmff to Visnu and Bhaqavata Puraqas the total comes out to be 850 years. 



54 ANCIENT INDIAN CHRONOLOGY 

above. Hence the time between the birth of Parlksit and the 
extinction of the Andhras becomes according to tbe Puranic 
=2354 jears. 

Now in the mode of reckoning time by the cycle of Rsis, 
the constellation of the great-bear is taken to remain conjoined 
with one naksatra for hundred years. In >23o4 years, the Rsis 
(Great Bear) would be taken to pass over 23 naks>itras and 
reach the 24th naksatra. This is thus stated in the verse L : 



\ 

r u 

* The seven Rsis were conjoined with Maghds 100 years in 
Pariksit's time ; they will be in the 24th constellation (naksatra) 
according to my estimate at the end of the Andhras.' 

Here we have a clear statement by the summarizer that 
between the birth of Pariksifc and the extinction of the Andhras 
the interval was slightly less than 2400 years. Hence it is 
clear that the true intention of the Puranic summarizer, as to 
the interval between the birth of Pariksit. and the accession of 
Mahapadrna, is that it was about 1500 years and the true reading 
of the second tulf of the second line of the verse in question is 
undoubtedly '^sf Msd^l'dH^. 5 ' 

We have now to consider the following Visnu and BMgavata 
statements that 

(a) c From the birth of Parlksit to the accession of Maha- 
padma Nanda the time interval is to be known as 1015 (or 1050) 
years. 2 

(&) * When the Great Bear will reach the naksatra Purvasadha, 
the Kali Age will have ascendency from the time of Nanda/ 8 

These verses cannot be traced either to the Matsya or the 
Vayu texts. They are at variance with the dynastic lists as given 
in the Visnu and the Bhdgavata Puranas. Even Sridhara, the 

1 Pargiter's Kali Age, pp. 58-59. 

2 tr: i ^4 *re a *^' 3 ^3 MWaOtKi n 

Pargiters Kali Age, p 58. 

*rftifcf n 

.; p. 61 



DATE OP THE BEABATA BATTLE 

great commentator of the Visnu Purdna, could not reconcile 
these statements and in the second statement would substitute 
< Pradyota ', the first king of the Pradyota dynasty in place of 
' Nanda.' l In these Puranas (Visnu and Bhagavata) the sum- 
marizes were crazy in their arithmetic, and the Purtnas them- 
selves were written most probably in the Gupta and post-Gupta 
periods, and are not at all trustworthy in so far as historical 
matter is concerned. The main aim of the composers or com- 
pilers of these Puranas was to inculcate Vaisnavism or the Visnu- 
cult and perhaps not to record any real history. 

If we are to put any faith in the Purdnic dynasty-lists and 
the Purdnic summarizes, the date of the Bharata battle becomes 
1921 B.C. as follows : 

Interval between Pariksit and Nanda - 1500 years 
Duration of the Nanda dynasty = 100 

Accession of Chandra Gupta Maurya = 321 B.C. 

The total gives the year == 1921 B.C. 

but we cannot accept as correct these Purdnic statements whether 
of the dynastic lists or of the Purdnic summarizers. The Brhad- 
ratha dynastic list is incomplete, further there was probably one 
period of interregnum between the extinction of the Brhadrathas 
of Magadha and the rise of Pradyotas of AvantL 

Again if we take that the ' future * Brhadrathas reigned for 
full 1000 years and the past Brhadrathas for 300 years, the 
dynastic lists would make the interval between the birth of 
Parlksit and the accession of Nanda 1900 years taking the inter- 
regnum to have lasted 100 years. To this period we have to 
add 421 to have the year of the Bharata battle, which would now 
stand at 2321 B.C. All such speculations are valueless or incon- 
clusive when they are based on totally unreliable materials derived 
from the Puranas. By way of contrast we have shown already, 



1 Cf. "siFlf^ffi I tT^cIt^ el^^H 1 

*rrwrf ^rf^T^^weErm i 
i 



fa 3ft' ^^*^t; I Srldhara's commentary on the 
Visnu-Purana, 



56 ANCIENT INDIAN CHRONOLOGY 

how neatly and directly the Mahabharata astronomical references 
lead us to the real year of the Bharata battle. 

If the Puranic faulty dynastic lists may lead us to 2:257 B.C., 
we should more readily and preferably accept 2449 B.C. as the 
true year of the Bharata battle, since it is deduced from the 
Mahabharata incidental statements, which are more definite and 
also consistent astronomically, and corroborated by the Vrddha 
Garga tradition as recorded by Varahamihira, 

(e) Further Puranic Evidences by the ' Position ' 
of the Great Bear 

[We now proceed to consider another alleged PnrSmc evidence 
which states the position of the Great Bear in Parlksit's time. 
To UB the statement that the Gieat Bear remains in one nakuatra 
for 100 years is meaningless ; still wo have to make some attempt 
at understanding wha* the Pumuas say about it* The Puranic 
description of the movement of the Great Bear runs thus I : 

' The two front stars of the Great Bear, which are seen 
when risen at night, the lunar constellation which is seen equally 
between them in the sky, the Great Bear Is to be known as 
conjoined with that constellation 100 years in the sky. This is 
the exposition of the conjunction of the lunar constellations and 
the Great Bear. The Great Bear was conjoined with the Maghas 
in Panksit's time 100 years. 1 * 

The two front stars are the two pointers, viz. <x and /? Ursae 
Majoris. We are to draw two great circles, one through each 
of the pointers and both passing through the celestial pole of 
the time : these circles will cut the ecliptic in two points; between 
these two points the naTcsatra in conjunction with the Great Bear 
be equally distinct. The Great Bear was conjoined with 



rft f*?f Wft Tjftpft 



r'u Kali Age, p. 59, 
* Pargiter's Kali Age, Truuslaliou on p, 75. 



DATE OF THE BHIRATA BATTLE 57 

the MayMs (a, y, y, , /uand e Leonis} in Pariksit's time according 
to the above Purdnic statement. This means that the celestial 
pole of the time of Parlksit lay on the great circle passing through 
the central star of the Maghds (a Leonis) and the middle point 
of the arc joining a and /3 Ursae Majoris. The celestial pole 
moves In a small circle about the pole of the ecliptic of a mean 
radius of about 23 30'. We have solved this problem and the 
time of this celestial event comes out to be 371 B. C. The above 
statement as to the alleged position of the Great Bear in 
Pariksit's time is also equivalent to this: that the right ascension 
of a Leonis was equal to the mean of the right ascensions of a and 
j8 Ursae Majoris. From Dr. Neugebauer's Stemtafelen (Leipzig, 
1912) the time for the event becomes about 300 B. C. It should 
thus appear that the time indicated by this Purdnic statement, 
as to the position of the Great Bear in Pariksit's time, belonged 
neither to Parlksit nor to this Purdnic astronomer. It is absolutely 
valueless for our purpose. Any other interpretations, that may 
be sought to be given to this position of the Great Bear as stated 
in the Purdnas in Pariksit's time, are not acceptable as they 
would be mere speculations. 

Some say that Saptarsi or Great Bear here means the solsti- 
'cial colure ; the compiler of the Purdna wants to say that the 
solstitial colure passed through the middle point of the line joining 
a and /3 Ursai Majoris at the time of Parlksit. According to the 
above interpretation the time of Parlksit stands at the neighbour- 
hood of 1400 B. C. But according to the statements of the 
Purdnas, the Saptarsi-tinQ passed not only through the middle 
point of a and /3 Ursai Majoris, but it also passed through the 
middle point of the naksatra Maghd at the time of Parlksit. So 
according to the Purdnas , the finding of time is not to be done 
with the help of a and ft Ursai Majoris alone, leaving aside the 
naksatra division Maghd or the star Regulus. On the other hand 
we can find out the time alone with the help of Maghd. It may 
be shown that the summer solstical colure passed through Maghd 
(Regulus) in 2350 B. 0.; but as the middle point of the na'ksatra 
Maghd is at about 40' east * of the star Regulus, -the time when 

1 According to the division of the ecliptic into nafyatras as is now accepted, 
8-4408B 



58 ANCIENT INDIAN CHRONOLOGY 

the solsticial colure bisected that naksatra division is 2398 B. C. 
which is very near to 2449 B. C. the year of the Bharata battle 
as determined by us. We have already said that an exact 
determination of the time of any past event by the above method 
IB not possible. It would be rather controversial and inconclusive 
if in interpreting any statement of the Pur anas we take into 
account only a portion of it. We have shown before that the 
Puranio statement regarding the position of the Great Bear is 
valueless. The year 371 B. C., obtained from the position of 
the Great Bear, perhaps Delates to the time when the Matsya and 
the Vdyu Purdnas began to be compiled, which has no connection 
with the time of Pariksit. 

We have thus most carefully examined the Puranio evidences 
as to the date of the Bharata battle. We have established that 
the oldest Purdnic strata are to be found in the Matsya Parana, 
then conies the Vdyu Purdna in sequence of time. In so far 
as historical matter is concerned the Visnu and Bhdgavata 
Purdnas are not at all trustworthy. Even in the Matsya Purdna 2 
the dynastic list of the Brhadrathas of Magadba is incomplete 
in that it states the names of the chief kings only and the dura- 
tions of their rules. We have also sean that the Purdnic sum- 
marizers really mean that the time interval between the birth 
of Pariksit and the accession of Mahapadma Nanda was about 
3 500 years. The Visnu and Bhdgavata summarizers' statement 
that the same period was about a thousand years is not reliable 
aa it contradicts the dynastic lists of these Puranas, cannot be 
traced to the Matsya and Vdyu Purdnas and not acceptable 
even to the great scholiast Sridhara of the Vi-snu Purdna. The 
incomplete dynastic lists of the Matsya Purdna properly inter- 
preted may lead us to 2321 B.C. as the year of Bharata battle. 
Any speculation with such faulty materials as the Purdnas afford, 
can never lead to the real truth about the year of the Bharata 
battle. On the other hand much better data have been derived 
by us from the Mahabharata itself which directly lead us to 
2449 B. C. as the Year of the Bharata battle and this was the 
zero year of the Judhisthira era according to the Vrddha Garga 
tradition. We hsiive also given the most careful consideration 



BATE OF THE BHAEATA BATTLE 53 

to the Puranic description of the position of the Great Bear in 
Pariksit's time. This only leads us to the year 371 B. C, a 
most hopelessly absurd result. Hence the Puranic evidences 
taken as a whole are incomplete and cannot lead us to the real 
year of the Bharata battle. We trust our interpretations of all 
these evidences would be found to be rational and compare 
favourably with those given by Pargiter, 1 Dev, 2 Bay, 3 Bose, 4 and 
others. 

Thus in the previous chapter we have shown that the Arya- 
bhata tradition, viz., 3102 B. C. as the year of the Bharata battle, 
is wrong. In the present chapter we have also established that 
the Puranic, evidences are all incomplete and inadequate for our 
purpose. The Mahabharata references lead us directly to the 
year 2449 B. C. as the year of the great battle. The Kaliyuga 
which the Mahabharata speaks of beginning from about the year 
of the Bharata battle truly started from the 10th January, 2454 
B. C. Even in the year of the battle (2449 B. C.) this Maha- 
bharata Kaliyuga may have begun from the 15th January, We 
may look for epigraphic evidences in this connection but none 
have been brought to light as yet. Let us hope ^that such may 
be discovered at no distant future, when only our- finding may be 
finally tested. Till then our finding of the year of the Bharata 
battle must be allowed to stand. 



i Pargiter's Indian Historical *T factitious The date of the Bharala baiil4. 

* Dov in JRASBL, 1925. 

3 prof. J. C. Kay in HKc^S for the Bengali jear 1340, NOB. 3, 4 and 5. 

* Dr. G. S, Bose in his T 



DATE OF THE BHAHATA RATTLB 31 

to the Puranio description of the position of the Great Bear in 
Pariksit's time. This only leads us to the year 371 B. C,~ a 
most hopelessly absurd result. Hence the Purdnic evidences 
taken as a whole are incomplete and cannot lead us to the real 
year of the Bharata battle. We trust our interpretations of all 
these evidences would be found to be rational and compare 
favourably with those given by Pargiter, 1 Dev, 2 Ray; 1 Bose, 4 and 
others. 

Thus in the previous chapter we have shown that the Arva- 
bhata tradition, viz., 3102 B. C. as the year of the Bharata battle, 
is wrong. In the present chapter we have also established that 
the Puranio evidences are all incomplete and inadequate for our 
purpose. The Mahabharata references lead us directly to the 
year 2449 B. C. as the year of the great battle. The Kaliyuya 
which the Mahabharata speaks of beginning from about the year 
of the Bharata battle truly started from the 10th January, 2454 
B. C. Even in the year of the battle (2449 B. C.) this Maha- 
bharata Kaliyuga may have begun from the 15th January. We 
may look for epigraphic evidences in this connection but none 
have been brought to light as yet. Let us hope v that such may 
be discovered at no distant future , when only our- finding may be 
finally tested. Till then our finding of the year of the Bharata 
battle must be allowed to stand. 



1 Pargiter 's Indian tHstorical Traditions The date of the Bliaraia battle. 

2 DM in JEASBL, 1925. 

3 Prof. J. C. Bay in qpflqct for the Bengali jear 1340, ftos. 3, 4 and 5. 
* Dr. G. S. Bose in his f^Jf^ in Bengali* 



CHAPTER IY 

yEDIC ANTIQUITY 
Madhu-Vidya or the Science of Spring . 

In our enquiry into the antiquity of the Vedas, we shall, as a 
first step, try to interpret the Madhu-Vidya or the Science of 
Spring of the Vedic Hindus. It may be objected at the outset 
that the term Madhu-Vidya may not really mean the Science of 
Spring as here translated. Our answer is that Madhu and 
Madhava were the two months of spring of the Vedic tropical 
year. 1 Hence there is some justification for putting Madhu- 
Vidya as equivalent to Science of Spring. I trust more reasons 
for this rendering into English of the word would be apparent 
with the development of this chapter 

To every Hindu the following Rcas are well-known : 

Bg-veda, M. I, 90, 6-8. 



* i *ncr : sFssft^n: u 
u 
n 



' Sweetness is blown by the winds and sweetness is discharged 
by the rivers ; may the herbs be full of sweetness to us. May 
the uights and twilights be sweet to us, may the dust of the 
earth be sweet, may the sky-father (Dyauspitr = Jupiter) to us be 
full of sweetness. May the trees be full of sweetness to us, may 
the sun be full of sweetness, may our kine be sweet to us.' 

The rsi here finds that with the advent of spring air becomes 
pleasant and the water of rivers delightful. This was the time 
for harvesting wheat and barley and he conjures up the herbs to 



'*nr*r 

Taittinya SaAihfta, 4, 4, ll t 



VEDIC ANTIQUITY 01 

yield him sweetness in the shape of a bumper crop. He expects 
the nights and twilights to lose the dullness of winter and be 
pleasant to him, and even the dust of the earth is to lose the cold 
touch of winter. He expects, the benign sty would yield him 
timely rain. The trees (then bearing flowers), the sun, the cattle 
are all to become full of sweetness. 

The elements which bring him happiness or sweetness are: 
(1) the winds, (2) the rivers, (3) the herbs, (4) the nights, (5) the 
twilights, (6) the earth, (7) the kindly sky bringing in timely rain, 
(8) the trees, (9) the sun, and (10) the cattle. 

In the Brhadaranyaka Upanisat, II, 5, 1 14, the elements 
bringing in sweetness or Madhu to all beings are elaborated and 
enumerated as : (1) the earth, (2) water, (3) fire, (4) the winds, 
(5) the sun, (6) the cardinal points of the horizon, (7) the moou, 
(8) lightning, (9) thunder, (10) the sky, (11) right action, (12) 
truth, (13) humanity, and (14) the self. Here the connection of 
the elements with the coming of spring is quite forgotten, but it 
is remembered that the Madhu-vidya or the science of spring was 
discovered by Tvastr from whom it passed to Dadhici who revealed 
this science to the A6vins after they had replaced the head of 
Dadhici with the head of a horse. This story was revealed to the 
rsi Kakslvan according to the Brhadaranyaka Upanisat. 

The "first verse quoted in this Upanisat is the re. M. I, 116, 
12 and runs as follows : 



< As thunder announces rain, I proclaim, leaders, for the sake 
of acquiring wealth, that great deed which you performed, when 
provided by you with the head of a horse, Dadhyafic, the son of 
Atharvan taught you tfie science of Madhu (i.e., spring)/ 

The next verse quoted by the Upanisat is $g*eda, M. I, 
117, 22, which is: 



62 ANCIENT INDIAN CHRONOLOGY 

'You replaced, Asvins, with the head of a horse, (the head of) 
Dadhici, the son of Atbarvan, and true to his promise he revealed 
to you the science of Madhu (spring) which he had learnt from 
Tvastr and which was a jealously guarded secret.' 

These lines from the Rg-veda suggest to us that the science of 
spring or Madhu-vidyd was nothing but the knowledge of the 
celestial signal for the coming of spring, What that signal was is 
now the matter for our consideration. 

The Aiivins are always spoken of and addressed in the dual 
number. The Vedic rsis most probably identified the Asvins with 
the stars a and /? Arietta tike prominent stars of the nahsaira 
Asvini. Whether this be true or not, this much is certain that 
the Asvins were and are even now regarded as the presiding deities 
of this naksatra Avirii. The three stars a, /3 and y Arietis form a 
constellation which is likened to the head of a horse. * The Asvins 
are spoken of as riding in the heavens in their triangular, 
three-wheeled and spring-bearing Chariot, in several places in the 
fyg-Veda, some of which are: 

(i) *OT qgpft siffingSt ^^frrer frrreigBw 35 fey > 

M. I, 34. 2 

' Three are the solid wheels of your spring -bearing (Madhu- 
Vdhana) chariot, as all the gods knew it to be when you attended 
on Vena (Venus ?) the beloved of Moon/ 

wt sfkrat srftRteflg gsn i 

n 



M. I, 157.3 

'May the three-wheeled car of the Asvins, -which is the 
harbinger of spring (Madhu-Vahana), drawn by swift horses, 
three canopied, filled with treasure, and every way auspicious, 
come to our presence and bring prosperity to our people and our 
cattle.* 



Sakalya Sdthhitd> II, 162. 

2 I am indebted to Prof. MM. Vidhu&khara, Sastri, the Head of the Dept. o'f 
Sanskrit, Calcutta University, for this and the next reference from the $g-Veda. I 
owe it fco him also that the adjective ^sfrer' ' Spring-bearing ' is applied only to 
the car of the ASvins tnd to the car of no other god in the $ 



VED1C ANTIQUITY 6B 

\ 

M. X,41. 2 

' Ascend, Nasatyas, your spring -bearing chariot which is har- 
nessed at dawn and set in motion at dawn, etc.* 



M. I, 34. 9 

* Where, Nasatyas, are tbe thiee wheels of your triangular 
. Where the three fastening and props (of the awning)? ' 

(Wilson) 



M. 1, 47. 2 

* Come A6vins, with your three-columned triangular car/ 

(Wilson) 



M. 1, 118. 2 

* Come to us with your tri-columnar, triangular, three-wheeled 
and well-constructed car.' (Wilson) 

All these references speak of the triangular, tri-columnar, 
three-wheeled car of the A^vins. Here the three wheels of the 
car of the Agvins were perhaps the three stars <x, /3, and 7 Arietis, 
which constitute the naksatra Afoini likened to the head of a 
horse. Most probably tbe car of the A^vins included one more 
star, <x Triangnlwn, which with <x and Arietis formed a stable 
solid triangle as shown in the figure given below. 

ASvins* A Car 



The first three references speak of the car of the A^vins a* 
or harbinger of spring. The third reference directly 



W ANCIENT INDIAN 

states that the car of the Abvins which is * spring-bearing ' is 
harnessed at dtiwn and set in muthm <// dawn. Inference is here 
irresistible that when the car of the A*vins, viz.. the constellation 
Avini consisting of the stars a, 3 and 7 Arietis became first visible 
at dawn, the season of spring began at the place of observation 
which we shall take to be of the latitude of Kuruksetra in the 
Punjab. 

According to Wilson, the A^vins were ' the precursors of the 
dawn, at which season they ought to be worshipped with liba- 
tions of Soma juice/ There are of course many passages in the 
Rg-Veda which justify the above statement made by Wilson, 
but we desist from quoting them here as they only tell us that 
first rose the Asvins, then came the dawn, and then rose the 
sun. 1 The season referred to here is that of the heliacal rising 
of the car of the Asvins which brought in spring. The jealously 
guarded ' Madhu-Vidya ' or the ' Science of Spring ' was thus 
nothing but the knowledge of the celestial signal for the advent 
of spring, and this was the heliacal rising of the stars <x, ft, y, 
Arieiis. Of these three, oc Arietis rises last. Hence the Asvins 
rise completely when oc Arieiis rises* 

For the beginning of the Indian spring, the sun should have 
the tropical longitude of 330. Henoe when the star oc Arietis 
became first visible at dawn it was the beginning of Indian spring 
with a celestial longitude of 330 for the sun at a place in the 
Punjab of which the latitude was the same as that of Kuruksetra 
(30* N). This furnishes sufficient data for the calculation of 
the time for this astronomical event. Now the dawn begins 
when the sun is 18 below the horizon. Thus at the time when 
ex Arietis reached the eastern horizon with the sun at 18 below 
the horizon, Madhu-Vidya was discovered or it was recognised 



1 Some of these references from the Jfg-Veda are noted below : 
<*) 3^f4 35 *fK?fa*t WJ ^319 ft * S?PF?rftraf*T I (M. I, 7, 4, 10) which 
meant * Before t&e dawn even, Savatri ssnda to bring you to the rite, your wonderful 
c*r shining with clari6ed butter/ (6) ^ro; ^jft TrfiFTMta: I (M. Ill, 5, 5, 1) 
i.e. ' the praiser awakes to glorify the Advios before the dawn/ These translations 
are due to Wilson, Cf. othr references : M. I, 5, 5 ; M. 1, 6, 7 ; M, 1,9,31,4; 
M. 1, 9, 4, 9 ; M. UI, 6, 5, 1 ; M. VII , 4. 14, 5; M. VIII, 1, 5, 2. 



VEDIC ANTIQUITY 81 

One thing more that strikes us in this connection is that the 
so-called horse of Indra was most probably the constellation Leo, 
which is ordinarily likened to a lion. It may be likened to a 
horse as well, as in the above diagram: 

The stars e, p, Leonis forming the head of Indra's horse, 
the line joining y and 8 Leonis the back, <x and Leonis the 
two legs, j8 Leonis the end of the tail. Indra in his car took 
his seat a little behind j3 Leonis. 

As I have said before, in the first Chapter on ' Madhu-Vidya,' 
it has been established that when the first visibility of the Avins 
in the east was the signal for the advent of spring, the time 
was about 4000 B.C. These two Chapters show that about 4000 
B.C the Vedic Hindus recognized the coming of the Indian 
spring and of the rains, by the heliacal risings of ex Arietis and 
ot Leonis respectively. 

This practice is similar to that of the ancient Egyptians, 
of reckoning the year by the heliacal rising of <x Canis Majoris or 
Sirius. In Homer's Iliad, we find in Bk. -V, that this star 
Sirius is called " the summer star which shines very brightly," at 
least thus the translator interprets it. Again in Iliad Bk. XXII, 
is mentioned a f star which rises in autumn ' which people call 
the " dog of Orion.' 9 It seems that the same star Sinus was both 
the summer star and the autumn star in Homer's time. In 
such a case very probably the first visibility of the star at dawn 
showed the beginning of summer in Greece and the position of 
the same star higher up at dawn, the beginning of autumn. 

It now appears that the practice of recognizing the seasons 
by the heliacal risings at some or other of the bright stars was 
followed by all ancient nations. 



11-U08B 



CHAPTER YI 

VEDIC ANTIQUITY 
Rbhus and Their Awakening by the Dog 

In the preceding two chapters, we have spoken of the cons- 
tellation of " the Car of the A6vins " and of " the Horse or the 
EJorses of Indra." In the present chapter we shall see who 
were the makers of the above constellations in the earliest Vedic 
times. The story of Dadhici will also appear as mere allegory 
from what follows. The Rbhus, whose deeds wo are going to 
describe here, were of the race of AOgiras and wore exceptionally 
brilliant men of those times and whilo living they wore entitled 
to the share of the sacrificial portion with the gods and after 
death they were supposed to be dwellers in the orb of the sun, 
The first hymn of the [Rg-Veda addressed to them is M. L 20, 
and here the Rsi is Medhatithi, and runs as follows 1 : 

1. " This hymn, the bestower of riches, has been addressed 
by the sages, with their own mouths,* to the (class of) divinities 
having birth." 

2. " They wHo created mentally for Indra the horses that 
are harnessed at his words, have partaken of the sacrifice per* 
formed with holy acts/ 1 

Here the ' horses ' of Indra may be a single-bodied but & 
two-headed horse, being represented by the constellation Leonu. 
An alternative interpretation would perhaps be that the two stars 
Castor and Pollux may have been taken for India's horses, while 
Indra (=Maghavan)' had his seat at ex Lconis (Magha). This 
interpretation would be in harmony with the Greek tradition of 



showi that thia hymn w*s not actually composed by M*dhititW t * 



VEDIC ANTIQUITY gg 

taking the stars Castor and Pollux as horsemen. Between 
cc Leon** and the stars Castor and Pollux, there lies no bright 
ecliptic star. These two stars rise before ex Leonfr, the seat of 
Indra, on whose heliacal rising at Kuruksetra the rains set in 
in those times. The next rcas of the hymn run as follows * : 

3. They constructed for the Nasatyas, a universally mov- 
ing and easy car, and a cow yielding milk/' 

Here the " car of the Agvins " was the star-group formed of 
the stars <x, ft and y Arietis together with ex Triangulum, of which 
<x and ft Arietis with <x Triangulum formed the stable triangle, 
<*, ft and y Arietis the head of the horse, while ex a nd fl Arietis 
were symbols for the A6vins. 

4. " The Rbhus, uttering unfailing prayers, endowed with 
rectitude and succeeding {in all pious acts)' made their parents 
young/' 

As we are concerned with the deeds of Rbhus we quote only 

6. " The $bhus have divided unto four the new ladle, the 
work of the divine Tvastr." 

8. " Offerers (of sacrifices)', they held (a mortal existence) ; 
by pious acts they obtained a share of sacrifices with the gods/' 

This hymn thus narrated the deeds of the Rbhus and the 
honoured position which they attained by those good deeds, tn'#., 
privilege of having the sacrificial portion with the gods. 

The next m to bear witness to the above great deeds of the 
Rbhus was Kutsa in the hymns M. I. 110-11. The most sig- 
nificant rcas are the following : 

4. " Associated with the priests, and quickly performing 
the holy rites, they, being yet mortals, acquired immortality and 
the eons of Sudhaavan, the Rbhus, brilliant as the sun, became 
connected .with the ceremonies of the year/ 1 3 



\\\\\ 



M. 1. 110, 4. 



84 ANCIENT INDIAN OHEONOLOGY 

The above verse shows the great esteem and position which 
the Ebhus had won while living amongst the men of their time. 

5. " Lauded by the bystanders, the Ebhus, with a sharp 
weapon, meted out the single sacrificial ladle, like a field 
(measured by a rod) , soliciting the best libations, and desiring 
to participate of sacrificial food amongst the gods." x 

6. "To the leaders (of the sacrifice), dwelling in the firma- 
ment, we present, as with a laddie, the appointed clarified butter 
and praise with knowledge those Rbhus, who, having equalled 
the velocity of the protector (of the universe, the sun), ascended 
to the region of heaven, through the offerings of sacrificial food." * 

Here the Ebhus are described as have ascended the orb of 
the sun by the merit of having offered the sacrificial food to the 
gods. We shall have further accounts of their life after death 
as understood by Dirghatamas and "Vamadeva. 

" The Ebhus, possessed of skill in their work, constructed for 
the A6vins a well-built car ; they framed the vigorous horses 
bearing Indra ; they gave youthful existence to their parents ; 
they gave to the calf its accompanying mother." 3 

We next pass on to the hymns of Dirghatamas of M. I. 161, 
the rcas 6, 11 and 13, 

" Indra has caparisoned his horses : the Agvins have har- 
nessed their car : Brhaspati has accepted the omniform cow : 
therefore, Ebhu, Yibhva and Vaja go to the gods, doers of good 
deeds, enjoy your sacrificial portion." 3 

Here the import is that' Indra begins to function or that 
the rains set in, when the constellation Leonis or Indra' s horse 
rises heliacally, and that the rising in the same way of the car 
of the A6vins brings in spring, and. Brhaspati or Jupiter has been 



t u *iT*tai*TO 
% f^4)^: u 

U. I. 110, 5 and 6. 



M. I. Ill, 1. 



M. 1. 161. 6. 



^ VBDIO ANTIQUITY 65 

discovered as a wandering body in the sky (here called the omni- 
form cow). These are indeed great deeds which entitled the 
Bbhus to enjoy the sacrificial portion with the gods. They 
were great as observers of the heavens who had discovered the 
celestial signals for the coming of the rains and of spring ; they 
had also discovered the planet Jupiter. 

" Bbhus, the leaders (of the rains), you have caused the grass 
to grow upon the high places ; you have caused the waters to 
flow over the low places ; for (the promotion of) good works : 
as you have reposed for a while in the dwelling of the unappre- 
hensible (unconcealable more properly) sun, so desist not to-day 
from the discharge of this your function/' l 

We conclude that the Bbhus were also leaders of the rainy 
season, they slept for a while in the orb of the sun with the first 
bursting in of the Indian summer monsoons, i.e., from the time 
of the summer solstice. Here the idea of sleep of the Ebhus at 
this time, formed the basis of the Puranic Hindu faith that 
Visnu and other gods sleep during the entire period of the rains 
lasting for four months of the Indian rains. At the place of the 
first Aryan settlers, which we have taken to have been near 
Kuruksetra, there was a clearing up of the sky for some time 
after this first bursting of rains. Here Dirghatamas does not 
tell us how long the Bbhus sleep in the orb of the sun, but that 
so long as they sleep the sky remains cloudy and the. grass grows 
on the high places and water is spread over the low places. In 
the next verse we are told that the Bbhus are awakened by the 
Dog when the clearing up of the~ sky follows the first bursting 
of the monsoons. 

" ?/bhus, reposing in the solar orb, you inquire, ' who awakens 
us, unapprehensible (unconcealable) 1 sun to this office of sending 
rain? ' Sun replies * the awakener is the Dog and in the year 
you again to-day light up this world.' " 2 



M.I. 161, 11* 
M. 1.161,13. 



86 ANCIENT INDIAN CHRONOLOGY 

Here the sun is taken to exhort the Rbhus reposing in his orb 
to clear up the sky on the call of the Dog. We are inclined to 
take, that this call of the Dog means the heliacal rising of the 
Dog-star or ex Canis Majoris, Sirius or the Sothis which was the 
Egyptian name of the star. 

We next pass on to the following re by Vanaadeva. 

" When the 5-bhus, reposing for twelve days, remained in 
the hospitality of the unconcealable sun, they rendered the fields 
fertile, they led forth the rivers, plants sprung upon the waste 
and waters spread over the low places.'* * 

'From this statement it appears that in Vamadeva's time, 
the Rbhus were taken to sleep for 12 days in the orb of the sun 
when they were awakened by the rising of the dog-star. 

Hence we conclude that in Vamadeva's time the heliacal rising 
of the dog-star took place twelve days after the sun reached the 
summer solstice. Now on the basis arrived at above, we 
determine the time of Vamadeva as shown below, supposing that 
he also lived at the latitude of Kuruksetra (30N) . 

At the time we are going to determine, the heliacal rising 
of Sirius (ex Canis Majoris) took place, at the latitude of Kuruk- 
setra, twelve days after the sun had reached the summer solstice. 
So the sun's true longitude was then 90 +12 or 102 nearly 
and the star came on the eastern horizon when the sun was 
18 below it. 

At the epoch 1931-0, the star oc-Oam* Majoris had its 

K.A. = 6h 42m 6-524 s. 
Dec.= -1687'13" 

and the obliquity of the ecliptic <o=:23 26'54" 
By transformation of the co-ordinates, we get : 

Long. = 1037'52* 

Lat. = -3935'24", this latitude is suppos- 
ed to remain nearly constant since the time of Vamadeva. 



u 

1C. IV. 837, 



VEDIC ANTIQUITY 87 




Let the above figure represent the observer's celestial sphere at 
the latitude of Kuruksetra (30N). Her HPZH' is the observer's 
meridian. HOEaH' the horizon, yEM the celestial equator and yLB 
the ecliptic. S, indicates the sun's position at 18 below the horizon 
and a is the . point on the horizon where a Cani* Majoris rose at that 
time. Z and P respectively denote the Zenith and the celestial pole 
of the observer. 

Now the following quantities are known: 

7&=true long, of the sun=102 ... ... (1) 

,/ EyS = obliquity of the ecliptic at the required epoch which is 
assumed to be about 2700 B.C.240 / ... ... ... (2) 

In the triangle ySM, the above two parts are known and the 



Hence the declination of the sun=SM=2327'N ... (3) 

and the R.A, =yU=>Wy& ... . ... (4) 

Now in the triangle ZPS, 

ZP=60, PS=6633' and 38=108. 
The angle ZPS is given by 



tan 



ZPS 




x sin ZS+PZ-PS 

** 



. , 

. ZS + PS+PZ .. ..._ PS+PZ-ZS ; 
on - - - xsin - g 



whence we find the ZZPS=129'46'. ... - (5) 

Subtract from it the ZZPE which is 90, we find the angle MPB 

orthearcME=39 46' ... - - - J 6 j 

Agam7E= r M-ME=103'6'-89'46'=63'20' , ... (7) 



68 ANCIENT INDIAN CHEONOLOGY 

Now in the triangle yEO, yE=632<y, 



So the other arc yO is found from 
cotyO x sin 6320'=cos 24 x cos 6320'-tan 30 X sin 24 



.-. cot 7 x sin 63*20' 



. , n 
. . cot vU = 

* 



cos 528''5 
cot6320'xcos768'-5 



cos 52 C 8'*5 
HenoeyO=7854/'6 ... ... ... (8) 

Again from the same triangle 

Sin yOE = sin 68 2Q/ x sin i20 
1 sin 7855' 

So the ZyOE=52 3'. ... ... (9) 

Lastly we come to the triangle aLO, 

where aL = 39 35' f 4 (latitude of the star) 
ZaOL=523' end the angle afc L is a rt. angle. 
Hence sin OL=tan aL x cot aOL 

.\OL=40 9'C'. ... ... (10) 

Now from the results (8) and (10) we can easily find the 
longitude of the star at the required epoch, thus : 

yO=7854''6 

OL=409'5 

.'. yL=98*46' 

= longitude at the required time. 
Long, in 1931'0 AJX=103 8' 
at the epoch= 3845' 

.*. Increase in the celestial long. = 6423 ; 

As a first approximation the above increase in the celestial 
longitude of the star indicates a lapse of 4636 years up to 
1931 A.IX 



VEDIC ANTIQUITY 97 

him the atmosphere, the spaces (rajas) were measured out ; by 
him the gods discovered immortality." * 

" 8. The ruddy one examined (vi-mrS) the all formed, 
collecting to himself the fore-ascents (praruha) and the ascents 
(ruha) ; having ascended the sky with great greatness, let him 
anoint thy kingdom with milk, with ghee/' 2 

"9. What ascents (ruha) fore-ascents (praruha) thou hast, 
what on-ascents (druha) thou hast with which thou fillest the sky, 
the atmosphere, with the brahman, with the milk of them 
increasing, do thou watch over the people in the kingdom of the 
ruddy one." 3 

In the first of these three verses, the heavens are divided 
into (1) svar, (2) naka, and perhaps also into (3) the atmosphere, 
and by the sun, it is stated that the spaces were measured out. 
Here by the word svar is meant the part of the celestial sphere 
between the two tropics and the remaining portion was named 
naka. 

In the second verse we, have the words ruha and praruha 
which must mean respectively the northern and southern limits 
of the sun's ascent as estimated on the meridian. All these 
considerations lead us to think that the " line of Brahma *' of the 
Atharva Veda and the Taittiriya Brdhmana was undoubtedly 
the winter solstitial colure passing through the star a Pegasi. 
Hence our finding the date of the earliest Vedic culture as 4000 
B.C. finds a most unexpected corroboration from the tradition 
recorded in the above-mentioned Vedic literature. It shows 
clearly that the earliest of the Vedic Hindus, the Rbhus, were 
interested principally in the determination of the solstitial colures 
and not much so in finding the equinoxial colures. The mention 
of Rohim as the first star in the Mahabharata and the mention 



f ffa 



TOW TOST 

13^4083 



98 ANCIENT INDIAN CHRONOLOGY 

of the two Rohinis in the Taittirlya Samhitd and the Taittirlya 
Brdhmana, with a difference of exactly 180 of longitude, suggests 
that the determination of the vernal equinox by the ancient 
(Vedic) Hindus could #ot have happened before 3050 B.C. The 
Mahabharata again speaks of the full moons at the Krttikds and 
the MagMs, and as these stars Krttikd (r\ Tauri) and Maghd 
(a Leonis) differ in longitude by alraost exactly 90 degrees, the 
above statement points accurately to the positions respectively 
of the V, Equinox and the summer solstice of the date 2350 B.C. 
although perhaps determined about 2449 B.C., the date of the 
Bharata battle which was also the date of the Taittirlya Samhitd, 
as it speaks of the Krttikds as the first naksatra. 

I tried to interpret the Atharva reference quoted above in 
terms of the heliacal rising of Pogasi with the sun at vernal 
equinox, conjoined with Rohim, but this interpretation was found 
impossible astronomically. 

In the Chapter on " Madhu-Vidya or the Science of Spring/' 
I have demonstrated that the Science of Spring was the knowledge 
that spring set in near about Kuruksetra with the heliacal rising 
of the Afoini group of stars, viz , the stars a, /? and y Arietis. The 
date from this condition, I have shown, comes out to be 4000 B.C 

The further confirmation of this finding of mine has also been 
.foupd from the Rg-Veda itself. Tn M J. 85, the verses 13-15 
run as follows 1 : 

"' Indra, with the bones of Dadhyanc, slew ninety times nine 
Vrtras." 

" Wishing for the horse's head hidden in the mountains, he 
found it at Saryanavat." 

" The (solar rays) found on this occasion the light of Tvastr 

verily concealed in the mansion of the moving moon." 

(Wilson), 



ef: i 



i a^raqre n l a 

I OTT 



I am idebted to Mrs, A.S.JX Maunder, F.R.A,S. for drawing my attention to these 
verses. 



VEDIC ANTIQUITY QCJ 

In Wilson's translation, the last verse should begin with 
" He " in place of " The (solar rays)." The first verse says that 
Indra slew his enemies called Vrtras (i.e., Clouds) , with the 
thunderbolt made of the bone of the fictitious parson Djiihyanc, 
as the tradition from the Paranas says. In the second verse 
Indra discovered that spring had just begun with the heliacal 
rising of the horse's head or Agvim cluster when he observed it 
from the lake Saryanavat which was near Kuruksetra according 
to the commentator. In the third verse the occasion or the time 
of observation was when Tvastr (=the sun) was found (or rather 
inferred to be) at the expected place of the moon or the night in 
question was of a new-moon. It must be admitted that a 
new-moon night is the best for observing the heliacal rising of a 
star or star group. It is almost needless to repeat that I used the 
same data for arriving at the date 4000 B.C. in the chapter on 
Madhu-Vidya. 

In another place of the Rg-Veda, Indra is called mesa (the 
ram) M.I. 51,1 runs thus l : 

"Animate with praise that Earn, Indra, who is adored by 

many, who is gratified' by hymns and is an ocean of wealth." 

Wilson. 

In explaining why Indra is called a ram (mesa), Wilson refers 
to a legend, in which it is narrated, that Indra came in the form 
of ram to the sacrifice solemnized by Medhatithi and drank the 
Soma juice. 

Now the sacrificial jear began with spring generally, hence 
Indra's coming to the sacrifice began by Medhatithi must mean 
the heliacal rising of Aries (rather the Asvinl cluster at the head 
of the Earn) at the beginning of spring. This is therefore easily 
interpreted by the Madhu-Vidya, and Medhatithi must be a very 
ancient rsi, much anterior to Varaadeva who flourished about 
2760 B.C. as determined in a previous chapter. 

It must be admitted that in the Rg-Vcda we have the 
mention of the constellations Mesa (Aries) and Vrsabha (Bull), 2 



, M. 1.116,18* 



loo ANCIENT INDIAN CHKONOLOGY 

which were quite forgotten or disused in the later Vedic times 
and also in the Vedangas. I have not got the names of the 
other signs of Zodiac in the Rg-Veda ; perhaps they were not all 
formed ia those days. I ha\re already pointed out the dropping 
of some other old constellations in the later Vedic literature, the 
Vedangas and the Mahabharata. 

It is perhaps unmistakably established that the earliest date 
for the Vedic Hindu culture must be about 4000 B.C. 



CHAPTER IX 

VEDIC ANTIQUITY 
The Solar Eclipse in the Rgveda and the date o/ Atri. 

In the present chapter we propose to find the time of the 
solar eclipse described in the Rg-Veda, th time which was 
undoubtedly that of the m Atri. who was the author of the 
hymn V 40 5-9. The first attempt at finding the date of this 
event was made by Ludwig l in May, 1885, with the assistance of 
the Viennese astronomer Oppolzer. Ludwig imagined that there 
were references to four eclipses of the sun in the JJj.Fb, *,* 
V 40 5-9; V, 33, 4; X. 138, 3a and X, 1*. 4. I * 
examined all these references and my view is that only 
the first reference describes a real eclipse of the sun the 



n w-n 

n 



in Mid 



iOMi 7*6 



b- 






,{ &'iea<* 

he ichte of tbe jsoneum*"- * * 

Paper published in bitz u y 
in 1885. 



102 ANCIENT INDIAN CHRONOLOGY 

on Rgveda V, 40 and its Buddhist parallel in Festscrifo Roth 187. 
Eclipse du Soliel par Svarbhanu, parallel Samyukta Nikdya, 
II, 1, 10, cited in Louis Benou's Bibliographie Vedique. 

We can only say that such similarity of statements as to 
solar eclipses in the two works cannot establish that the Atri 
tradition was contemporary with the Samyukta Nikaya event. 
To settle chronology by a reference to a solar eclipse is a very 
difficult matter, no easy-going researches can be of any value. 
Without making further attempt at tracing all the different 
attempts made before by other researchers, we proceed to 
interpret the Rgveda reference V, 40, 5-9. The original Sanskrit 
rca's are : 



i 



1 ^ i 

is I 



Wilson's translation runs as follows : 

**5. When O Surya, the son of asura, Svarbhanu, over- 
spread (rather 'struck') thee with darkness, the worlds were 
beheld like one bewildered not knowing his place." 

The second line perhaps is more correctly translated as, 
** the worlds shone lustreless like a confounded tactless person." 

" 6. When, Indra, thou wast dissipating those illusions of 
Svarbhanu which were spread below the sun, then Atri, by his 
fourth sacred prayer (turiyena brahmana), discovered (rather 
'rescued') the sun concealed by the darkness impeding his 
functions." 

Whitney explains that Svarbhdnu means simply "sky-light.** 
Whatever that may be, what interests us here is the phrase 
" turlyeya brahmana," "by the fourth sacred prayer", as trans- 
lated by Wilson after Sayaija. Some say that this means a 



VEDIC ANTIQUITY 103 

quadrant or the fourth part of a graduated circle, which we 
cannot take to be correct. The use of the graduated circle, 
or its fourth part in Vedic times was an impossibility ; we could 
admit the validity of the interpretation if the event belonged 
to Brahmagupta's time (628 A.D.). Further it is a barren 
meaning throwing no light on any circumstance of the eclipse. 
As Wilson following Sayana translates the phrase as " by the 
fourth sacred prayer,' * we may take this to be the only correct 
interpretation. As the fourth prayer of the day, most likely 
belonged to the fourth part of the day, we interpret that the 
eclipse in question was finished in the fourth part of the day. 

Again the phrase 'turiyena, brahmand.' may also be inter- 
preted in a different way. The word ' brahman ' itself may mean 
the summer solstice day. In the Sfolkhdyana Iranyaka (Keith's 
translation), the Mahilvrata day is spoken of as " This day is 
'Brahman' ([, 2) and again the same day is thus referred to, 
" Brahman is this day" ( 1, 18). In the Jaiminiya Brdhmana, 
II, 400-10, we have 



which means that the maktivrata ceremony used to be performed 
on the Vixuvant or the summer solstice day* We thus under- 
stand that 4t turiyena brahtnand" means "by the fourth part 
of the nnmmer solstice day-" In other words, the eclipse in 
question was over in the fourth part of the summer solstice 
day itself. (Mere "turiyena brahmand turiyena Mlena 
brahmadivastina." "Brahman" thus means the longest day of 
year, which seems quite natural). 

"7. fKurya speaks] ; Let not the violater, Atri, through 
hanger, swallow with fearful (darkness) me who am thine ; 
thuti art Mttra whose wealth is truth : do thou and the royal 
Varuna both protect me." 

Thi verse seems to suggest that the eclipse in question 
although apprehended to be total was not so at the place of the 
observer. Atri is here spoken of as having saved the sun from 
total disappearance. The verse is perhaps an example of 
"wisdom or power after the event." 

"8. Then the Brahmana (Atri), applying the stones together, 
propitiating the gods with praise, and adoring them with 



104 ANCIENT INDIAN CHRONOLOGY 

reverence, placed the eye of Stir y a (sun) in the sky ; he dissipated 
the delusions of Svarbhanu." 

Here Atri is alleged to have found out the instant of the end 
of eclipse by counting stones together a practice which was 
continued even up to the time of Prfchudaka (864 A.I).). 1 
Atri's placing 'the eye of Surya in the sky shows that the end 
of the eclipse'was visible or the eclpse finished before sunset. 

"9. The sun, whom the asura Svarbhanu enveloped (rather 
'struck') with darkness, the sons of Atri subsequently recovered ; 
no others were able (to effect bis release).'* 

As t;> the day of the year on which this eclipse took place, 
the'Kaufitaki Brdhmana, (xxiv, 3, 4) throws clearer light: 



159* 



V 



Keith translates the passage as follows : 

"Svarbhanu, an Asura, pierced with darkness the sun ; the 
Atris were fain to smite away its darkness ; they performed, 
before the Visuvant, this set of three days, with saptadasa 
(seventeen) stoma. They smote away the darkness in front 
of it ; that settled behind, they performed the same 
three day rite after the Visuvant ; they sniote away the darkness 
behind it. Those who perform knowing thus, this three-day 
(rite) with the Saptadaa stoma on both sides of the Visuvant, 
verily those sacrificers smite away evil from both worlds. They 
call them the Svarasdmans ; by them the Atris rescued (apas- 
prnv&ta) the sun from the darknesss ; in that they rescued, 
therefore, are the Svarasamans, This is declared in a re. 

1 <?/. Calcutta University Publication of tfce Khandakhadyaha, with 
Coxnxndntary, page 16. 



VEDIC ANTIQUITY 105 

" The sun which Svarbhanu 

The Asura pierced with darkness, 
The Atris found it, 
None other could do so." 

We gather from this passage that the day on which the 
eclipse happened wa=t the Visuvant day. Now the word 
* Visuvant, 9 according to the Aitareya and the Kausitaki 
Brahmanas, meant the summer solstbe day, as I have set forth 
elsewhere. The arguments may be summarised thus : 

According to the Aitareya Brahmana, the Visuvant and the 
EkavirhSa day was the same day, ths day on which the gods 
raised up the sun to the highest point in the heavens, and that 
on this day the sun being held on either side by a period of 10 
days (Virdj) did not waver though he went over these worlds. 
Or that the Visuvant was the true summer solstice day. The 
Kausitaki Brahmana also says that the sun starting northward 
from the winter solstice on the new^moon day of Magha, reached 
the Visuvant after six months. Thus according these two Bjf- 
Veda Brahmanas the Visuvant day meant the s, s. day only. 

In the days of the Taittiriya8amhit& 2446 B.C. and the Tandya 

Brahmana (about 1700 B.C.), the word Visuvant came to mean 

the middle day of the sacrificial year begun from spring, <tt it 

became the day when the sun's longitude became 150, i.e., 

the beginning of the Indian autumn. Finally the same word 

came to mean about the fcima (1400 B.C.) of the VedfiAgas* the 

vernal or the autumnal equinox day. The question to settle is 

which of these three meanings should we accept for the correct 

interpretation of this Rgvedic reference. Hence in interpreting 

a Rgveda reference, we should take the word Visuvant as the 

summer solstice day only, as this is the meaning of it given by 

the Rgveda Brahmanas. Another point that needs be clarified 

is to get at the rough time of Atri and the place of his observation 

of this eclipse. We shall use the Rgveda references alone. 

As to Atri, there are many references in the Rgveda : 

I 51, 3 ; 1, 112, 7 ; 1, 116, 8 ; I, 119, 6 ; I, 139, 9 ; 

1,180,4; 1,183,5; V, 73, 6-7 ; VII, 68, 5 ; VII, 71, 5; 

1 Yajusa Jyautisam, 23. 
H_1408B 



106 ANCIENT INDIAN CHEONOLOGY 

VIII, 35, 19 ; VIII, 36, 7 ; VIII, 37, 7 ; VIII, 42, 5 ; VII, 
62, 3-8 ; X, 39, 9 ; X, 143, 1-8 ; X, 150, 5. 

Some of them are cited below as evidence to show where 
and when Atri lived. 

(a) I, 51, 3 addressed to Indra 

"Thou hast shown the way to Atri, who vexes his adversaries 
by a hundred doors." l 

(b) I, 112, 7 addressed to the Agvins 

" You rendered the scorching heat pleasurable to Atri." 2 

(c) I, 119, 6 addressed to the A^vins 

"You quenched with snow (Uimena) for Atri, the scorching 
heat/' 3 

(d) I, 116, 8, addressed to the Advins 

"You quenched with cold (himena), the blazing flames (that 
encompassed Atri), and supplied him with food-supported 
strength ; you extricated him, Avins, from the dark cavern into 
which he had been thrown headlong, and restored him to every 
kind of welfare.'* 4 

(e) I, 139, 9, addressed by Parucchepa to Agni, showing the 
high antiquity in which Atri lived. 

" The ancient Dadhyane, Angiras, Priyamedha, Kagva, Atri 
and Manu have known my birth " 5 
(/) I, 181, 4 to the ASvins 

" You rendered the heat as soothing as sweet butter to Atri." 6 
(0}V, 73, 6-7 to the Advins : 

" Leaders (of rites), Atri recognized your benevolence with a 
grateful mind on account of the relief you afforded him, when, 



5 ^sisFfft *t*[$ ^ffs^ffro: ftrfr?t ^nsffs^rf^ft^f^?^ ^p^P'ft n 



8 



V&DIC ANTIQUITY 10? 

Nasatyas, through his praise of you, he found the fiery heat 
innocuous." fci Atri was rescued by your acts." l 

From these quotations it would appear that Atri took shelter 
in a cave with a hundred doors or openings, where he felt 
scorching heat, which was allayed by a thaw of ice from the 
snow-capped top of the mountain peak, at the bottom of which 
this cave was situated. From the quotation (e), we gather th?it 
Atri was a contemporary of Dadhyanc, Augiras, Priyamedba, 
Kanva and Manu, was probably one of the first batch of Aryans 
to pour into the Punjab. The favour of the AiSvins which Atri 
is alleged to have received was at the time perhaps of the rising 
of a Arictifi in the east at the end of evening twilight. For this 
astronomical event at about 4000 B.C. at the latitude of 
Kurukaetra, the Sun's longitude comes out to have been 97 54', 
which was correct to about 8 days after the simmer solstice the 
time or part of the year which was quite favourable for the 
thaw of the Himalayan ice. 

We may then conclude that Atri lived about the time 
4000 B.C., in a cave of hundred openings at the bottom of a 
snow-capped peak either of the Himalayas or of the Karakoram 
range. Hence the eclipse of the sun spoken of in the hymn 
attributed to Atri, happened on the Visumint or the summer 
solstice day either correctly ascertained or estimated, in the 
fourth part of the day of the meridian of Kuruketra, 

I, Now the Visuvanl day as correctly ascertained would be 
the true summer solstice day, as we have reasons to believe that 
its ascertainment was possible for the Vedic people. Next if we 
suppose that as the Yedic year was of 306 days, the B.S. day was 
estimated from an observational determination of it one year 
before, the estimated B.S. day would tend to fall on the day 
following the true S.S. day. Hence we have to understand that 
by the word Visiwanl, we arc to understand either the true S. 



108 ANCIENT INDIAN CHRONOLOGY 

Solstice day or the day following it, if we suppose that both the 
winter and summer solstice days were truly determined by the 
Vedic calendar makers of those times. 

2. Then again if we suppose that the W. Solstice day was 
correctly ascertained by observation as a new-moon day of Macjha, 
and the summer solstice day was always estimated, the so-called 
S.S, day of those tincns would have many variants. The 
Kausltaki Brahmana, the Aitareya Brahmana and the 
Veddngas take the sun's northerly and southerly courses to 
be of equal durations. This is possible only when the sun 3 s 
apogee has the longitude of 90 or -270. In the actual case the 
variation is shown below : 

Half year from Half year from 

Year. W. Solstice to S. Solstice to 

S. Solstice. W. Solstice. 

4000 A.D. 187 days 178'24 days 

3000 A.D. 186-75 178' 49 

2000 A.D. 186*10 179'14 

1000 A.D. 185-20 180*04 " 



The following interpretations may consequently be put on 
the Visuvant day of Vedic literature : 

^a) If the eclipse happened about 4000 B.C., on the estimated 
S. Solstice day from an accurate determination of the W. Solstice 
day on a Magrfoa-new-mdon day, in 21 years (tropical) the number 
of days would correctly be = 917 or even 918 days: whereas 
according to the Vedic calendais the same period would comprise 
915 days only. Hence the estimated S. Solstice day would be 
2 or 3 dqys before the true date. 

*(b) If about 4003 B.C., the eclipse happened on the estimated 
S. Solstice day, under the same system of reckoning for 7$ years 
(tropical), the number of days in this period =2744 days correct 
and in the Vedic calendar there would be 2745 days instead. 
'Hence the estimated S. Solstice day would be the day fallowing 
the true S, Solstice day. 



VEDIO ANTIQUITY 109 

Hence in looking for the solar eclipse on the Visuvant day 
as interpreted in 1 and 2 (b) above, we must take it to mean 
either the true summer solstice day or the day following it. 

In the case 2 (a) we shall have to look for the eclipse 2 or 3 
days before the true S. Solstice day; in this case we would be 
content on pointing out the suitable eclipse or eclipses. The 
detailed study will be made in the other case only. 

We begin with former cases which are the more important 
for many reasons set forth before. 

Hence the solar eclipse we \*ant to find the date of , must 
satisfy the following conditions: 

(1) It must have happened on the summer solstice day or on 
the day following and no other date is admissible. 

(2) It must have been a central solar eclipse. 

(3; It must have happened or rather ended in the fourth part 
of the day for the meridian of Kuruksetra. 

(4) It must have been observed from a cave at the foot of a 
snow capped peak either of the Himalayas or of the Karakoram 
Kange. 

(5) That at the place of Atri, the eclipse did not reach the 
totality. 

(6) It must have happened between 4000 to 2400 B.C., 
neither earlier nor later, when the word Visuvant had its oldest 
meaning, viz., the summer solstice day. 

We now proceed to determine the central solar eclipse which 
must satisfy all the conditions enumerated above. We get at a 
central solar eclipse happening on the 21st July, 3146 B.C. 

The Kausltaki Brdhmana says that the sun turned north on 
the new moon of Mdgha. This Mdgha is not an ordinary month 
of Mdgha as it comes every year, but it was the Vedic standard 
month of Mdgha, which "came in our times in the years 1924, 
1927, 1932 and 1935, as has been shown in another place. 
I tried the months of Mdgha of the years 1924, 1932, and 1935, 
but these did not lead to a central solar eclipse. The Vedic 
month of Mtujlia as it came in the year 1927 B.C., however, 
did yield the central solar eclipse on the 21st July, 3146 B,C,, 



110 , ANCIENT INDIAN CHRONOLOGY* 

on the day following the summer solstice day in tbe following 
way : 

In the year 1927 A.D,, the Vedic standard month of Mdgha 
lasted from February, *2 to March, 3, half the Vedic lustrum or 
full 31 lunations after this date came the 3rd of September, 
1929 A.D., on which day the new moon happened at about 
Gk M. noon. 

Now on the 3rd September, 3929, G-.M.N., the sun's mean 
longitude from Newcomb's equation comes out to have been 
162 8' 33". Ignoring the sun's equation I assumed as a first 
step that this longitude was =90 at the year we want to 
determine. This shows a total shifting of the solstices by 
72 8' 33", representing a lapse of 5227 years till 1929 A.D. 
From which we get that the longitude of the sun's apogee was 
12 36' 48" at 51'98 centuries before 3900 A.D. The eccentricity 
of the sun's orbit was ='01858 nearly. Hence the sun's 
equation for the mean longitude of 90 was -2 5' 9" nearly. 
This equation is applied to the mean longitude of the sun at 
G.M.N. on the 3rd September, 1929, viz., to 162 8' 32". The 
result 160 3' for 1929 A.D, was =90 in the year we want to 
determine. This gives a total shifting of the solstice up to 
1929 A.D. to be=70 3 ; nearly, indicating a lapse of 5074 years. 
Now since 5074 =1939 x*2 + 160x7 + 19x4, and as 1939, 160 and 
19 years are lunisolar cycles, it may be inferred that the number 
of elapsed years till 1929 A.D. does not require any change to 
make the year arrived at similar to 1929 A.D. 

Now 5074 sidereal years =1853311 days 

= 5074 Julian years + 82'5 days. 
Hence the Julian date arrived at 

= -3145 A.D. July, ,20. 
or =3146 B.C. July, 20. 



Now on July, 20. 
3146 B.C., G.M.N. 

(1) 

Mean Suo=9151' 48'/'42 
Mean Moon=80l' 41"'45 
Moon's Node=27021' 25* '00 
Moon's Perigee =25039' 1"*02 



and on July, 21, 3146 B.C., 



G.M.N. 



(2) 



Mean Sun=92 50' 56"*75 
Mean Moon =93 12' 16"'45 
Moan's D. Node=90 18' 14"'37 
Moon's Perigee=250 46' 42' / '07 



VBDIO ANTIQUITY 111 

The sua and the moon's elemaiits have been calculated back 
from the equations given by Newcomb and Brown, respectively, 
which have been taken as correct from 4500 B.C. up to the 
modern times. 

The figures in column (2) show that on fehe 21st July, 
31.46 B.G,, there was an annular eclipse of the sun, but this was 
not visible from the northern Punjab, and cannot be accepted as 
giving us Atri's time. This eclipse took place (1) on the day 
following the summer solstice, (2) in the 4th part of the day on 
the meridian of Kuruksetra, We take this eclipse as the starting ff 
point for further calculations. We find that : 

The mean tropical year at 3140 B.C. 305 -2425084 days 
The moan synodic month 3146 B,C.29'5305088 days 
The moan motion of the moon's node 

at this epoch = 696S6"'659C per tropical year. 
The tropical revolution of tho node for the 

same epoch = 18*61 127 tropical years. 
The tropical revolution of the moon's perigee 

at the epoch = 8 '84527 tropical years. 

In our calculations both backward and forward from this 
epoch, we cannot use the Chaldean saros as it does not contain 
an exact nntnber of tropical years. We have to proceed as 
follows : 

We want to find only those central eclipses of the sun which 
happened on the same <lay (&/#., the summer solstice) of the 
tropical year. 

Now, 

/ * Tropical year ^jo* | JL L -JL L- 

v Synodic month* " 2+ "l+ 2+ 1+ 1+ 18+ '" 

12 25 37 136 235 4366 
'Ihuconvc^ntHim-: T * a .g > g > Tr > jg ,353 

The important luni-solar cycles in tropical years are 8, 11, 19, 
and 353, the lunations in them being 99, 136, 235 and 4366, 
respectively. 



112 ANCIENT INDIAN CHRONOLOGY 

(b) The convergents to tropical semi-revolutions of the node in 
tropical years 

__ 28 93 121 335 

1 ' 3 ' 10 ' 13 ' 36 ' 

Now from these last set of canvergents we get, 
456 years=(335 + 121) 

= (853 +19x5 + 8) years. 

(1) .*. 456 years=_4i revols. of Node 

=5640 lunations very nearly. 
Aga'n 456 years = 166551 days 

and 6640 lunations=166552'6 days. 

(2) 391 years=(335 + 2 x 28) years 

= (36 + 6) nodal half revolutions 

=21 nodal revols. 

= (353+19x2) years. 
Again 391 years =142810 days 

and 4836 lunations = 142810 days. 
(3.) 763 y ears = (335 x 2 + 930) years=41 revols. of Node 

= (353 x 2+ 19 x 3) years =9437 lunations nearly. 
Again 763 years=278680 dajs and 9437 lunations =278680 clays. 

From these we readily get the new set of Cycles : 
= 4601 lunations 



372 tropical years 



= 20 re vol. 401' of motion of the Node 



= 42 re vol. + 20 of motion of Perigee 
= 4836 lunations 
391 tropical years \ =21 revol, + 310' of motion of Sode 

= 44 revol. + 7332' of motion of Perigee 



VEBIC ANTIQUITY 

Longitudes of Sun 

A 



B 



Mean Sun 
Sun's apogee 



92 21' 0" 
1 55 57 



92 25' 55" 
1 55 57 



121 



G 

92 S3' 51" 
1 55 57 



g = Sua'san:>inaly(Iadian)= 90 25' 3'' 90 29' 58" 90 34' 54" 
-128''977Siag = -2 8' 58* -2 8' 58" -2 8' 58" 
+ l'-512Sin 2g = ... -1 ... 



-2 



Mean 



MEAN ARGUMENTS 



Apparent Sun 90 12' 1" 90 l& 55" 90 21' 51" 
L Var. per hour ... 2' 27"'5 



Longitude of Moon 
A 



1 = Moon Perigee 


= 


346 


31' 


42* 


847 


37' 


1" 


348 


42' 


2F 


2Z 


= 


333 


,'i 


23 


335 


14 


2 


337 


24 


42 


D = Moon SUD 


s= 


357 


46 


46 


358 


47 


43 


359 


48 


40 


2D 


= 


355 


38 


32 


357 


35 


26 


359 


$7 


20 


4D 


= 


351 


7 


4 


855 


10 


52 


359 


14 


40 


?'= Sun Sun's perigee 


= 


270 


25 


8 


270 


29 


58 


270 


34 


54 


F 


=s 


173 


30 


18 


174 


36 


27 


175 


42 


36 


2P 


= 


347 





36 


349 


12 


54 


351 


25 


12 


2D-Z 





9 


1' 


50" 


9 


58' 


25" 


10 


54' 


59" 


2D-2Z 


= 


22 C 


30 


8 


22 


21 


24 


22 


12 


39 


2D-Z-Z' 


= 


98 


36 


47 


99 


28 


26 


100 


20 


5 


2D + Z 


= 


342 


5 


14 


345 


12 


27 


348 


19 


40 


2D-Z' 


= 


85 


8 


29 


87 


5 


28 


89 


2 


27 


Z-Z/ 


= 


-76 


6 


39 


77 


7 


3 


78 


7 


27 


l+V 


= 


256 


56 


45 


258 


7 





259 


17 


15 


2F-Z 


= 





28 


54 


1 


35 


53 


2 


42 


52 


2D-2F 


8 32 


56 


8 


22 


32 


8 


12 


8 


4D-Z 


= 


4 


35 


22 


7 


33 


61 


10 


32 


20 



Moon's Inequalities 
A 



B 



+ 22640 Sin I = - 

+ 769 Sin 2? = - 

+ 4586- Sin (2D-Z) = + 

-125 Sin D = + 

+ 2370 Sin 2D = - 

-. 669 Sin V + 

+ 312Sin (2D-2Z) = + 

+206Sin(2D-Z-Z') = + 

+ 192'Sin(2D+Z) - 

+ 165Sm(2D-Z') = + 

16-1408B 



5274"-3 


-4855"'0 


-4434//-0 


348-4 


- 3221 


- 295-4 


719-8 


-h 794'3 


+ 868-5 


4'8 


+ 2-6 


+ 0'4 


183-5 


- 99-6 


15*6 


669'0 


+ 669-0 


+ 669-0 


81*1 


+ 80-6 


+ 801 


203-7 


+ 203*2 


+ 202-7 


591 


- 49-0 


- 38-8 


164-4 


+ 164-8 


+ 165-0 



122 ANCIENT INDIAN CHRONOLOGY 

A B C 

+ 148Sin(Z-Z') = + 143-7 -I- 144'3 + 144'8 

-110Sin(Z + Z') = + 107-2 + 107'7 + 1081 

-85Sin(2F-Z) = - 0'7 - 2'4 - 4'0 

+ 59Sin(2D-2JF) - + 8'8 + 8'6 + 8'4 

+ 39Sm(4D-7) = + 31 + 51 + 71 

-ves = -5866-0 -53281 -4787'8 

+ VBB = +2105-6 +2180-2 +2254'! 

Total - -3760.0 -8147*9 -2533'7 

_ -l2'40"'4 -052'27"'9 -0 42' 13"*7 

Mean Moon = 90 7 45'4 91 13 38'3 92 19 31'2 

Moon on orbit = 89 5' o>0 90 21' 10"'9 91 37' 17'5 

A. Node (O) = 276 37 271 276 37 11'2 276 36 55'4 

P^M-O - 172 27' 37"'9 173 43' 59"'2 175 0' 22"! 

2F X = 344 55 15'8 847 27 58'4 350 44'2 

= -15 4' 44" -12 32' 2" -9 59' 16" 

-417Sin2F l = +0 1' 48'5 +0 1 30'5 +0" 1' 12"'3 

Moon on orbit = 89 5 5'0 90 21 10'4 91 37 17'5 

Apparent Moon - 89 6 58'5 90 22' 40'9 91 38' 29'"8 

Mean variation per hour ... 37' 54*1 

Instant of conjunction is 9'8 mins. before B. 

i.e. 9 hrs. 50 mins. A.M. G.M.T. or 2 hrs. 58 mins. P.M. Kuru- 

k?etra time 

Arguments for Latitude of Moon 

ABC 

T = 172 27' 38* 173 48' 59" 175 0' 22" 

2D-2F = 8 32 56 8 22 82 8 12 8" 

F +2D + 2F = 181 84 182 6 31 183 12 30 

V 1 ** 270 25 3 270 29 58 270 34 54 

F _Z/ = 262 2 35 263 14 1 264 25 28 

at + V = 82 52 41 84 13 57 85 35 15 

I 1 =346 31 42 347 37 1 348 42 21 

y _Z = 185 55 56 186 6 58 186 18 1 

F J _2Z = 199 24 14 198 29 57 197 35 40 

T +2D-2F-Z' = 270 35 31 271 36 33 272 37 86 

F!+2D-1F+Z' = 91 25 37 92 36 29 93 47 24 

F +2D-2F-Z ~ 194 2952 1942930 194 30 9 



VfcDlC ANTIQUITY 
Latitude of Moon 



123 



A 


B 


C 


+ 18518'5 Sin F x = + 2429'7" 


+ 2021"'o 


+ 1612"-0 


+ 528*3 Sin (F! + 2D-2F) 






- 93 


- 19-4 


- 29-6 


-25-0 Sin (Fi-Z') = +24'7 


+ 24-8 


+ 24'9 


+23*8 Sin (Fj + Z') = +23'6 


+ 23'7 


+ 23*7 


+ 23*2 Sin (FjZ) = 2*4 


2*5 


- 2-6 


-23-6 Sin (Fi- 27) = + 7'8 


+ 7'5 


+ 7*1 


+22-1 Sin (FJ + 2D-2F-ZO 






2F I'} ~ 22 ' 1 


-22-1 


- 2-2-1 


-10*4 


-10'4 


- 10-4 


- 15-4 Sin (Fj + 2D ~ 2F - 1) 






= + 3*9 


+ 3*9 


+ 39 


+ ves = +2489-7 


+ 2081*4 


+ 1671-6 


-ves = -44*2 


-54'4 


-64-7 


Total = +2445'5 


+ 2027-0 


+ 1606-9 


/. Latitude = +42'45^'5 


+ 33' 47-0 


+ 26' 46*-9 



Mean variation per hour = 3' 29""6 

Moon's horizontal parallax 

P=3422-''7 + 186"'6 cos Z + 10^'2 cos 2Z + 34"'3 cos (2D-Z) 
+ 280-3 cos 2D + 3"*1 cos(2D + Z) 

B 

+ 186-6 cos Z= +182*3 

+ 10-2 cos 2Z=* + 9-3 

+ 34-3 cos (2D-Zj=+ 33 '8 
+ 28'3ooscD= + 28-3 



Constant =3422-7 

Hor. parallax*86W'4=61' 1V4 

Moon's Semi-diameter- 16' 42"*4 

Sun f s Semi-diameter = 16' 1"*4 



124 ANCIENT INDIAN CHEONOLOGY 

Calculation of the eclipse for longitude of Kuruksvtra and 
latitude = 33 i North. 

ABC 

Mean Long, of Sun =92 21' 0'' 92 25' 55" 92 30' 51" 
Loca] time = 1-8 P.M. 3-8 P.M. 0-8 P.M. 

Local in degrees =17 47 77 

It. A. of meridian or 

Sidereal time =109 21' 01' 139 25 55 169 30' 51" 

Obliquity of the ecliptic = 24 & 15" 

Long, of culminating 

pt. of ecliptic = 107 46' 25'' 136 50' 5" 168 32' 16" 

Eclip. angle with meri- 

dian (0i) = 82 13' 23" 71 55' 36" G6 19' 23" 

Dec. of cul. point =+22 53' 11" +16 18' 25'' + 4 39' 18" 
Lat. of place =+33 30' 0" +88 8<X 0" <-33 80' 0" 

Z. dist. of cul. pt.= 

ZC = 10 36' 49" 17 16' 35" 28 50' 42" 

Z. dist. of Nonagesitnal 

=ZN - 10 31' 9" 16 23' 58" 26 13' 18" 

Parallax in lat. = - ll'll'"8 - 17'18"'9 - 27' 6"'0 

Lat. of Moon = + 40'45"'5 + 33'47"'0 + 26'46"'9 

Corrected latitude = + 29'33"'7 + 16'28"'l - 0'19"'l 

ABO 
Z. dist. of nonagesimal 

=ZN = 10 31' 9 r/ 16 23' 58" 26 13' 1 8" 

Z. dist. of cul. pt.= 

ZC = 10 36' 49" 17 16' 35" 28 50' 42" 

V = 82 13' 23" 71 55' 36" 66 19' 23" 

Cul. pt, nonagesimal 

= 1 27' 9" 5 30' 40" 12 28' 19" 



Culminating point * 107 46' 25" 136 50' 5" 168 32' 



VEDIC ANTIQUITY l3 js 

ABC 

V Nonagesimal =tf= 106 10' 16" 131 19' W 156 D 3' 57" 

App. Sun j= 90 12' 1* 90 1C' 55" 90 21' 31* 

N-@ = ltt 7' 15* 41 2' 30" 65 42' G" 

ZN = 10 81' 9" 16 23' 58" 26 18' 18" 

Parall. in Long. = - 16' 44"*4 - 38' 37"'6 - 50' 8"*4 

Long, of Moon = 89 6 53*5 90' 22' 40'9 91 38' 29* -8 

Corrected Moon = 88 50' 9"*1 89 44' 3 fft 3 90 48 ; 21""4 

App. Sun - 90 12 1 90 16 55 90 ? 21 51 

)- = -1 21' 52" -0" 32' 52" +0 26' 80" 

Istdiff. = +49' 0" +59' 22" 

2nd diflc . == + 10' 22" 



Where t is measured from B in units of 2 hrs. 

Corrected latitude = + 29' 33"'7 + 16' 28* '1 -0' 19"*1 
IsbdiS. = -13>5"-6 -Iff 47^2 

2nd diff. = -3' 41" '6 

Corrected latitude =16' 28"'1-(14' 56"'4)t-(l' 50"'8)f a =^ 

Sum of Semi-diameters =1964" (M+S) 
Difi. of Semi-diameters = 41" (M-S) 
Kuruksetra mean time. X ^ v'^+^ 2 

3-8 P.M. -1972* +988" 2206" 

-837 

3-38 o -1140 +757 1369 

-791 

4.8 , -269 +512 578 

1 ' +311 +1692 

4-38 +640 +254 689 

+ 901 

5-8 +1390 -19 1590 

5-38 +2577 -305 2595 



126 ANCIENT INDIAN CHRONOLOGY 

Nearest approach of the centres of the Sun and the Moon occurs 
37 x30 mins after 4-8 P.M., i.e., at 4*49 P.M. 
Minimum distance =521" 
Mag. of eclipse = *73o=8'8 [ndian units. 



Time of beginning=3 hrs. 8 mins.-f 

=3 hrs, 8 mias.-M) mins. =^-17 P.M, 
Time of ending=5 hrs, 8 mins. + 1 ^ 4 ^- 1 ~ x 30 mtn*. 

lOOt) 

= 5 hrs. 8 mins. + 11 mins,^ hr*.- W win*. P.M. 
The same Calculations for lui. of />/Cf = &"> c i A". 

A B 

Long.ofcul.pt. = 107 46' h 2;V lli(V J fllK ,V JOH" 'J' 10" 

^ = 82 13' #*" 71" ;>.V 8W HO" IU' US'' 

Dec.ofcul.pt. =+22r>8 f IP +10 13' 2.V j-4 ,'!' l8 /r 

Lat, of place =+35 30' 0" 4-35 ao' ^ 4-H:* 8^ (>" 

Z. dist. of cuL pt 

=ZC 12 :V 44V 10 10' 85" *> J' 42 /r 

Z. dist. of nonagesimul 

=ZN = 12 29' ii" 18 17' 2a" #4 W a> 

Parall. ia lat. - 18' 10''1 - 10' 14"'7 - 2K' -t7'''7 

Moon's lat. =* -h 4<X 45^3 -f JW47*'0 -h V Wit 

Corrected lat. -h 27' 2i)"'4 *h 14' 8^*3 - *J' <)"H 

Z. dist. of cul. pt. 

=zc 12 3ti' 4w ff iu" io' :jv ;wr r*o' 42" 

y = 82 13' 23" 71 .W 3(V 19' a.1" 

CuL pfc.-nonagesimal 

=CN * l* 44/ 4// e c 11' 32" 18' W '," 

Cul. pt. = 107 4ff a3 ff 1^30 5IK 3 1UH JfcJ' 10* 

Nonagesimal = 100 2' 21" 130 88' 8U" i;*5 12' 7" 

App. Sun s 90* 12' I" 90 10' r>5" W 21' ;*!'' 

Nonagesinal-Sun * 15 50' 20" JO" 21' JJH" 04 ax I0 n 
Z. dist. of nonagesimal 

*ZN a 12 ay' 44" 18 17' 25* 28* IK iiU* 



VEDIC ANTIQUITY 
Horizontal parallax of (Moon Sun) =3670'' '6 



127 



Parallax in long 

Long, of Moon 

Corrected Long 

Sun 

)- . - 

1st diff. 
2nd diff. 
/. )--* 

Corrected lat. 

1st diff, 
2nd diff. 
Corrected lat. = 



= - 16'18"'l - 37'36"'9 - 48' 53"! 

= 89 6' 53*5 90 22' 40"'9 91 38' 29"'8 

= 88 50' 35"*4 8 45' 4"-0 90 49' 36"'7 

90 12' 1* 90 16' 55" 90 21 51 

= -1 21' 26" -0 31' 51" +0 27' 46" 
= -4886" -1911" +1666" 

= +2975" +3577" 

+ 602" 

=* - 191 1" + 32772 + 301 t 2 whrere t is 
measured in units of 2 hrs. from B. 

= + 27' 29" + 14' 32" - 2' 1" 
+ 1649" +872" -121" 

-777 -993 

- -216 

/ = +872" -885 t-108t s 

Sum of Semi-diameters =1964"(M + S) 



Diff. ,. 



41"(M-S) 



ksetr a mean time . X ^ V X 2 + ^ 2 


3-8 P.M. 


. -1911" 


+ 872" 


2101* 


-422 


3-23 


-1497 


+ 760 


1679 












-428 


3-38 ,. 


-1073 


+ 644 


1251 


-423 


3-53 ,, 


-640 


+ 525 


828 


-379 


4-8 


-198 


+403 


449 




Tt v ) ) 








-73 


4-23 


+ 254 


+ 277 


376 


4354 


4-38 ,, 


+ 715 


+ 148 


730 


+ 456 


4-53 ,, 


+ 1186 


+ 15 


1186 


+ 484 


5-8 r . 


+ 1666 


-121 


1670 


+ 502 


5-23 ,, 


+ 2156 


-260 


2172 





+ 306 
+ 427 



128 ANCIENT INDIAN CHRONOLOGY 

Time of beginning^ ^ 2101 7* 964 x 15 mins. = 4*87 mins. 

4r,a 

after 8-8 P.M, /,., at 3-13 P.M. 

Time of endmg= 1964 7 167 *15 mins. = 8*79 mips 
o02 

after 5-8 P.M., i.e., at 5-17 P.M. 

Duration o eclipse = 2 hrs. 4 mins. . 

Neiresfc approash of the, centre* 361* at 4-18 P.M. 

Mag ot ejlipse=0*792=9'5 Indian unils. 

APPENDIX III . 

A Note on a Method 

of 
Finding a Central Solar eclipse near a Past Date 

The problem of the chapter to which thisJis an appendix, was 
tofin3 a central solar eclipse jm the summer, solstice day, visible 
in the northern Punjab, within the range 4000 B.C. to 2400 B.C. 
As shown in 'the -body of the paper a centr.il solar eclipse 
happening on the~'2l8t. July, 3146 B.C., obtained by a pure 
chance formed^ the starting poinfc for farther calculations. 
A method now occurs to me which shows that a cbronologist 
need not -depend upon any such chance. Further he need not 
also depend on a book like Oppolzer's in which all eclipses are 
calculates from - 1200 B.C. up to, the modern times. The 
equations .for the moon's elements used by Oppolzer were those 
given by Hanen, which have been thrown away by inter- 
national astronomers. Hence Oppolzer '_s great work has become 
more or less valueless. We have now to use Newcomb's 
equations for the sun's elements and Brown's for those of the 
moon. To undertake another great work like that of Oppolzer 
with the most up to date system, of astronomical constants 
should be now considered unnecessary on the score of the labour 
it entails, in the light of the elegant method presented in 
this note. 



VEDIC ANTIQUITY 129 

Problem 1. To find a central solar eclrpse near the date 

4000 B.C. happening on the summer solstice day and visible 
from the northern Punjab, 

Here we are to remember that the longitude of the ascending 
node should be about 85 or that of the descending node about 
95, on the day of the eclipse if this is to be visible from the 
northern Punjab. 

(a) We first work out the shifting of the equinoxes from 

4001 B.C. to the present time, say 1940 A.D. This works out 
to have been 82 27 7 23" nearly. Hence what was 90 of the 
longitude of the sun in 4001 B.C., would become 172 27' 23" in 
1940. The sun has this longitude now about the 16th 
September. 

(b) Now on looking up the nautical almanacs, we find that 
there was a new-moon on the 15th September, 1936. 

(<5) Again from 4001 B.C. to 1940 A.D., the number of years 
elapsed -5940. The correct luni-solar cycles in sidereal years are 
1939 and 160 years 

Now 5940=1939 x 3 + 123. 

Hence the elapsed years 5940, have to be increased by 37 years 
and we have, 

5977=1939x3 + 160, 

(d) We then apply 5977 sidereal years or 2183137 days back- 
ward to the date, 15th September, 1936, and arrive at the date 
4042 B.C., July, 26. 

(e) On this date OKM.N., the longitude of the moon's 
ascending node was=321 42/ 36-82, 

(/) We now use the eclipse cycle of 19 tropical years in 
which the node's position is decreased by 7 32' nearly. We 
want to reduce the longitude of 321 43' of the node to about 
275 c i.e., by 46 43' which comprises 732' six times nearly. 
Hence we have to come down 19 x 6 or 114 years. The year 
arrived at is 3928 B.C. Calculation of the eclipse on the 
summer solstice day of this year may now proceed as shown 
in the body of the paper, remembering that in 114 years 
(tropical) there are 41638 days K 

17 H08B 



180 ANCIENT INDIAN CHRONOLOGY 

Problem 2. To find the central solar eclipse which happened 
on the autumnal equinox day visible in the northern Punjab and 
near about the year 1400 B.C. 

On the autumnal equinox day the sun attains the longitude of 
180. In order thai the eclipse may be visible in the northern 
Punjab, the ascending node should have a longitude of about 
175 or the descending node 185 nearly. 

(a) From 1401 B.C. till 1940 A.D. the shifting of the 
equinoxes becomes 46 17' 26". Hence what was 180 of the 
longitude of the sun in 1401 B.C. has become 226" 17' 26" in 
present times. This corresponds to the date of November, 10 
of our times. 

(&) On looking up nautical almanacs we can find that a new- 
moon happened on November, 10, 1931 A.D. 

(c) Now the elapsed years 3340, till 1940 A JX need be 
adjusted a little as before; we have to increase it by 39 years, 
and we have, 

3379=1939+160x9. 

(d) We apply to the 10th November, 1931 A JX, 3379 sidereal 
years or 1234201 days backward, and arrive at the date 1449 B.C. 
October, 5. 

(e) On this date the longitude of the ascending node at 
G.M.N. was=201 2' 23*. 

(/) We have to reduce this longitude of the node to 175 
nearly by using our eclipse cycles. Now by our cycle of 19 
years, repeated four times, we can reduce it by 30 8' to 170 
54' by coming down to 1373 B.C. We have now to raise it 
from 170 54' by a further coming down by the eclipse cycle of 
372 years, to 175 15' nearly for the autumnal equinox day of 
the year 1001 B.C., as in Oppolzer's finding. 

Altogether we had to come down by 19 x 4 4- 372 =448 tropical 
years. 

Hence by the method thus illustrated, we can find near 
about any past date, any sort of solar eclipse we have any record 
of, however vague it may be. There is thus no necessity for 
finding all the solar eclipses from so far back a date as 4000 B.Q. 
up to our modern times. 



VEDIC ANTIQUITY 131 

I trust the attention of astronomers and chronologists all 
over the world, will be drawn to the method presented here for 
finding an eclipse of a back date, and hope they would further 
develop it and remove from it any flaws that they may discover. 



VEDIC ANTIQUITY 

Heliacal Rising of X and v Scorpionis in Atharva Ved* 

In the Atharva Veda 1 the heliacal rising of the two stars 
A and v Scorpionis is mentioned in II, 8 and III, 7. We quote 
the first verse as translated and annotated by Whitney, It is 
almost the same verse that is repeated in the two hymns which 
were used in incantations for relief from the disease Ksetriya. 1 

" Arisen are the two blessed stars called imfasteners (Vicrta) ; 
let them unfasten (Vimuc) of the Ksetriya the lowest, the highest 
fetter." 

Whitney's note runs as follows : 

* The disease Ksetriya (lit'ly, of the field) is treated elsewhere, 
especially in iii, 7 ^mentioned also in ii. 10 ; 14*5 ; iv. 18*7). 
The commentator defines it here as apparently an infectious 
disorder, of various forms, appearing in a whole family or perhaps 
endemic. The name Vicrtau, 'the two unfastners' is given 
later to the two stars in the sting of the Scorpion (A and v 
Scorpionis), and there seems to be no good reasons to doubt that 
they are the ones here intended ; the selection of two so 
inconspicuous stars is not any more .strange than the appeal to 
stars at all ; the commentator identifies them with Mula, which 
is the asterism composed of the scorpion's tail." 

Whitney concludes by " Their (the two stars) healing virtue 
would doubtless be connected with the meteorological conditions 
of the time at which their heliacal rising takes place ".* 



A. V, II, 8, 1. 



A. y. m, 7, 4, 



VEDIC ANTIQUITY 

According to Sayana, ksetriya diseases are Phthisis, Leprosy, 
Epilepsy, Hysteria and the like. We feel that the diseases 
included under this name Ksetriya are those skin and lung 
diseases which are aggravated by rainy weather and are relieved 
by the dry atmospheric conditions which follow the rainy season. 
The sore toes which the cultivators have in the rainy season 
are perhaps also included under the name Ksetriya. The season- 
beginning indicated by the heliacal rising of A and v Scorpionis 
was that of Hemanta or the dewy season. 

In Indian astronomy , there are recognised six seasons in the 
twelve months of the year, commencing from the winter solstice 
day and they are named winter, spring, summer, rains, autumn 
and Hemanta or the dewy season. The seasons, rains and 
autumn comprise four months which are called Varsika in 
Sanskrit literature, during which the gods are supposed to sleep. 
These four months are called Varsika (rainy) months in the 
Ramayana*. Thus the sun's celestial longitude at the end of 
these four months becomes 210, when the sky is finally 
'released' from the clouds according to the estimate of the 
Sanskrit authors. 

That the true heliacal rising of the stars A, and v Scorpionis 
is meant is seen from the following verses with Whitney's com- 
mentary. 

"Let this night fade away (apa-vas) ; lot the bewitchers 
fade away ; let the Jfseinya-effacing (-natiana) plant fade the 
Ksetriya away/* 1 

" In the fading out of the asterisms, in the fading out of the 
dawns also, from us fade out all that is of evil nature, fade out 
the Ksetriya. 9 " 

* Burgess* S&ryasiddMnta, VHI, 9, notes on the Uula 'junction star.* 



A. y. II, 8. 2. 



184 



ANCIENT INDIAN CfiBONOLOGtf 



Whitney's note : 

"The night at the time of dawn is meant, says the Com- 
mentator (doubtless correctly) According to Kau the hymn 

accompanies a dousing with prepared water outside the house ; 
with this verse it is to be done at the end of the night." 

Thus there is no doubt that the true heliacal rising of the 
stars A and v Scorpionis is meant. Although the two stars are 
inconspicuous according to "Whitney, the position of the two 
stars at the end of the tail of Scorpionis is remarkable to any 
watcher of the heavens, as they are very close together, marking 
the end of the tail. The astronomical data is now that there was 
a time in the Vedic (Atharvan) Hindu culture when the heliacal 
rising of A Scorpionis marked the coining of Hemanta or the Dew- 
season with the sun having the celestial longitude of 210. We 
take Kuruksetra, as before, for the place of observation, which 
has a latitude of 30N> 

For 1934, the star A Scorpionis had its 

Mean right ascension = 17 hrs. 29 mins. 7*437 sees., and the mean 
declination = 37 3' 26"*59 sees., while the obliquity of the ecliptic, 
<BT = 23 26' 52"*33. 

Hence for 1934, the celestial longitude of the star = 263 39' 50" 
and the celestial latitude = -13 46' 46*. 

The obliquity of the ecliptic for 3400 B.C., our assumed date, was 
24 3' 42". 

Now when the sun's longitude was 210 the right ascension was 
= 207 C 47' 6V, and the declination was. -11 45' 46". 




YEDIC ANTIQUITY 135 

Let the above figure represent the celestial sphere of the observer 
at Kuruksetra, HPZH' the meridian, H'AKEH the horizon; S the 
position of the sun at 18 below the horizon, P the celestial pole and 
Z the zenith. A is the point of the east horizon where the star A 
Scorpwni* rose. Here rNKS is the ecliptic. Join Z8 and PS by 
arcs of great circles, PS cutting the celestial equator at the point M, 
From A draw AN perpendicular to the ecliptic. We want to 
determine 



Now ZP = <>0 , ZS 108, PS = 90 +8 = 101 45' 46", ^-S 
30% S-M = 27 47' 61*, / KEflb - colatitude = 60 and AN = 
ia rt 40'40". 

0) In the triangle ZPS, the three sides ZP, ZS and PS are 
known. Hence the angle ZPS comes out to be = 104 8' 16" 

and the ZZPE is 90 degrees 
the arc EM * 14 8' 18* 
Now ^M as found already 27 47' 51* 
/. rE 13 39' 45". 

(2) In the triangle R-^K, the four consecutive parts are : 

/ KK-a- ~ 60, E-^a 13 39' 45", L E^K = 24 3' 42'/ 

and rK. 
Hcntio we find A*K 11 52' 44" and the 

aiwlu K 88 29' 23". 
(3; Now from the triangle ANK, we find 

that KN B 1 30' 13". 
Finally f;K 11 y 44" 

NK * rS6'18", 
.\ ^N 10 IV 31". 

V 

Hence celestial longitude of A Scorpionia at the required past 
date was IHO* 10' 31". Now in 1934, the same was = 263 39' 50" 
or the increase in tJie celestial longitude of the star A Scorpionis 
- 7 28' l ff . 

The moan precesaion rate 49"'6761. 

Hence the number of years elapsed till 19*'J4 A. D.= 5318, 
ignoring the proper motion of the star. Thus the date becomes 
3385 B.C, 



136 ANCIENT INDIAN OHEONOLOGY 

We have here worked out the date for a tradition about the 
beginning of autumn at the latitude of Kuruksetra : but we 
cannot say that this was the da f e of the entire Atharva Veda 
Further we are not sure if the observer's place was 30N latitude. 
If we suppose that the observation was made at about 2oN, 
the date arrived at would not lower it by more than a hundred 
years. Hence the Atharva Veda in some of its portions was 
begun about 3400 B.C. Although this Veda is traditionally 
later than the Rg-Veda, some portions of it are undoubtedly 
earlier than the tenth Mandala of the Rg veda and must be dated 
at about 2449 B.C., the date of the Bharata battle. 



CHAPTER XI 

VEDIC ANTIQUITY 
Varna and his Two Dogs 

The Vedic god Yama was the Lord of the Pitrs (the departed 
Fathers) and son of Vivasvant (Sun). In the Avestic literature 
he is Yima, the son of Vivanghat (Vendiad, Fargard II, 1, 2 etc.). 
The Pitrs or manes were or are the souls of the departed and 
according to a Hindu's daily ceremony of libation offering to his 
forefathers are classed into Agnisvattas, Saumyas, Havismanta, 
Usmapds, Saukalins, Barhisads and the Ijyapas. In the Rg- 
veda, however, we get the names of the Fathers as Barhisads, 
Saumyas and the Agnisvattas only. According to Wilson in 
Manu they are also termed Agnisvattas, Barhisads and the 
Saumyas. These Pitrs are invoked by the libation offerers 
as protectors. If the order of the Pitrs be the lower, the upper 
and the intermediate, their names are perhaps Barhisads, 
Saumyas and Agnisvattas (Rg-Veda) in tire same order. Now- 
a-days the orders of the Pitrs has been increased into seven, 
the addition being the orders Havismantas f Usmapas, Ajyapas 
and the Saukalins. Jt does not interest us for the present to 
enquire when these additions were made in the Hindu faith, 
We are here concerned with the faith about their place of abode 
and of their Lord Yama. On this point the Satapatha Brahman 
says : 

" ' Two worlds in truth there are,* they say, the 'world of the 
gods' and the 'world of the Fathers' (Pitrs). 99 l 

" The world of the gods is in the north and the world of 
the Fathers (Pitrs) in the south." 2 



, XIT, 7, 3> 7. 
-J&M. 



J8-WQ8B 



138 ANCIENT INDIAN OHHONOLOGY 

Thus the Pitrs live in the south, consequently their Lord Yama 
must also be a dweller of the south. In a modern Sanskrit 
Dictionary, Yama is defined to be 'a god appointed by the 
Supreme Lord for deciding the destinies of departed souls 
according to their good or bad deeds in this world of ours, and 

is stationed in the south.' In the Mahdbhdrata, Vanaparva, in 
the story of Savitri, it is said that 'Yama having bound the soul 
of Satyavan went southward.' In another Sanskrit Dictionary 
Yama is defined as 'the lord of the southern direction/ 
Hence according. to-the Hindu faith both Yama and his subjects, 
the Pitrs, are dwellers of the south. The Sanskrit word 'Yamya' 
meaning the south, is derived from Yama, the lord of the south. 

The Hmdu when offering libations to his fathers,- has 
to turn to the south and invoke them by the following verse : 

" Our fathers, the Saumyas and the Agnisvdttas come by the 
Devayana route (northward direction) be delighted at the sacrifice 
by enjoying our offering (Svadhd) and bless us. May they 
protect us," 1 ' 

There are the two routes spoken of in the Hindu sacred 
lore, the one is -the Devayana and the other the Pitrydna, 
respectively the route of the gods and the route of the 
Fathers. When the Fathers come, they come by -the Devayana, 
route and when they go back, . they certainly, follow the 
Pitrydna route. Thus both the- routes may lie on the 
same meridian, the former is the northward direction and the 
latter the southward direction. Here we have -to differ from Tilak 
who in the -book Orion would interpret that Devayana route is 
the part of the ..ecliptic lying north of the -celestial equator and 
the Pitrydna route, the part of the - ecliptic south of the 
celestial equator. His interpretation appears to be unjustifiable 
and incorrect, as the Fathers who corne from the south do 
follow according to the Hindu faith the Devayana route. 

When men die they follow according to Hindu faith the 
Pitrydna route or the southern direction. In this . route to the 
abode of Yama, lay two dogs which were both ** spotted four-eyed 



T: fwc*. 



VEDIC ANTIQUITY m 

dogs/' The Eg.veda verses ' addressed to the souls of men 
just departed run thus 1 : 

Pass by a secure path beyond the two spotted four-eyed 
dogs, the progeny of Sarama, and join the wise Pitrs who rejoice 
fully with Yama." ' 

" Entrust him, king, to thy two dogs, which are thy 
protectors, Yama, the four-eyed guardians of the road, renowned 
by men, and grant him prosperity and health," (Wilson) 

In the Athana Veda also the corresponding verses are 2 : 

" Bun thou paet the two four-eyed, brindled dogs of Sarama, 
by a happy road ; then go to the beneficent Fathers, who revel 
in common revelry with Yama." 

" What two' defending dogs thou has, Yama, four eyed, 
sitting by the road, men watching, with them, King, do thou 
surround him ; assign to him well-being and freedom from 
disease." (Whitney) 

These two dogs we take to have been the two stars a Cam's 
minoris and a Cam's majoris. The astronomical interpretation 
becomes that there was a time, Vedic or pre-Vedic, when these 
two stars pointed to the south celestial pole, i.e., at that time 
these two stars crossed the meridian simultaneously or they had 
the same right ascension. We now investigate this problem of 
determining this past time astronmically. 

The places of these stars for 1931 A.D are given as follows 
in the Nautical Almanac. 



Star 


Eight Assension - 


Declination 


a Canis Majoris 
a Cam's Minoris 


6* 42 m 6**524 
7 35 41*405 


-16 87' 13" 
5 24' 11" 



IUH 



i ?TWT- 
^ tf% UH $g-Veda, x, 14, 10.11. 

| ^T 



\\i\\\ 



*F 1F 



Veda, XVHI, 2, 



140 



ANCIENT INDIAN CHBONOLOOY 



The mean obliquity of the ecliptic was 23 26' 54" in 1931 AJD. 
Hence by transformation of co-ordinates, we get: 



Star 


Celestial longitude 


Celestial latitude 


a Canis Majoris 
a Canis Minoris 


103 7' 52* 
114 50' Off 


-39 35' 24" 
-16 <y24" 




In the above figure of the celestial sphere, let yC^ be the 
ecliptic, JT the pole of the ecliptic, P the celestial pole and O 
the summer solstice in 1931 A,D. Let <r x and o- 2 be the positions 
of a Canis Majoris and a Canis Minoris in 1931. Let o-j and <r 2 
be joined by an arc of a great circle cutting the path of the 
celestial pole in P'. Then P was the pole of the equator at 
the required time. The angle P*rp represents] the shifting of 
the solstices. 

(1) In the triangle ;r<r z o- 2 the four consecutive parts are i 

Ztr^Tr, ovr=90 -f3935 / 24 // , Z. 0-^0-3 == 11 42'8'', 
aroj 90H-160'24" 

/. we get, 

cot ovr l5 r x sin ll42 / 8' / 

= cos 11 42' 8" xsin 39 85' 24* -tan 16 0' 24" 

x cos 39 35' 24". 



VFDIC ANTIQUITY 141 

Now put eot f - ^^ffag /. f = 16 19' 43". 

Hence we get, 

t ^ tan 16 0' 24" x sin 23 IS' 41" 

2 * sin 11 42' 8" x sin 16 19' 43" 

.'. O-^TT = 26 42' 55". 

(2) Again in the triangle o-^P', the value of dP ; was very nearly 
24 7 7 32" about 4350 B.C. The four consecutive parts are : 

Z Povr = 26 42' 55", IK^ = 90 +39 35' 24", 
L o-^P', dP = 24 7' 32". 



We get readily, 

sin o-jjrP x cot 26 42' 55" -cos cr^P' x sin 39 6 35' 24" 
= cot 24 8' 42" x cos 39? 32' 24", 

Put cot 9 = cot 26 42/ 55// 
sin 39 36' 24" 

then = 17 47' 0". 
Hence we get, 

sin (ovrP'-0) = sin 6 x cot 24 7' 32" x cot 39 85' 24" 
/. o- 1 jrP'=17 47' 0" + 55 33' 5" = 73 20' 5" 

The celestial longitude of a Cams Majoris (1931 A.D.) 
= 103 7' 52" 

Hence the celestial longitude of P' for 1931 A.D. 
= 103 7' 52" + 73 20' 5" = 176 27' 57". 

.'. the L P?rP' or the shifting of the summer solstitial point 
up to 1931 A.D. 176 27' 57" -90 ~ 86 27' 57". 

The elapsed time thus coixies out to be 6280 years till 1931 
A.D. and the required dale is, therefore, 4350 B.C. 

Second Method. 

We can follow a second method to determine the past time 
when a Canis Majoris and <* Corns Minoris had the same right 



142 



ANCIENT INDIAN CHKONOLOGY 



ascension. In Dr. Neugebauer's Sterntafelen, the right ascen- 
sions and declinations of stars are given at intervals of 100 years, 
extending from 4000 B.C. downwards. We tabulate the right 
ascenisons of these two stars from -3600 to -4000 A.D. 



Year 


E. A. of 


E. A. of 


Difference 


2nd. diff. 




a Oani8 Majoris 


a Cam's Minoris 






-3600 


40 '12 


41 -66 


1'54 












17 


-3700 


39'04 


40*41 


1-37 












16 


-3800 


37'96 


' 89-17 


1-21 












16 


-3900 


36*88 


37-93 


1-05 












16 


-4000 


35*80 


36*69 


0'89 





From a comparison of the second differences we find that 
these become steady from -3700 A.D. at the rate of 0*16 per 
hundred years. Hence the difference between the right ascen- 

89 



sions of the two stars would vanish 



16 



x 100 years or ,556 



years before -4000. A.D. i.e. at about 4557 B.C. 

There is thus a difference of about 200 years in the two 
determinations of the time of the event by the two methods ; 
but I trust the date obtained before viz. 4350 B.C. is the more 
correct, as it is based on the elements of these stars determined 
by using more accurate instruments in recent times. Another 
point that needs be considered here is this : What must have 
been the initial error of observation in this connection. 

Now let us see what could have been the initial error if the 
epoch for the observation be taken as 4000 B.C. 

The total shifting of the equinoxes during the interval of 
5930 years between 4000 B.C. to 1931 A.D. = 8142'50''. If 
this be subtracted from the celestial longitudes of the stare for 
1931 A.D,, we get their position in 4000 B.C. Hence the^ 



VEDIC ANTIQUITY 



143 



celestial co-ordinates of the stars in 4000 B.C. are as follows 
(supposing the latitude to remain the same throughout) : 



Star 


Celestial longitude 


Celestial latitude 


a Oanis Majoris 
a Cams Minoris 


21 24' 59" 
33 7' Iff 


-39 35' 24" 
-16 (V 24" 



In 4000 B.C. the obliquity of the ecliptic was i-24 6'35". 
Hence by transformation of the co-ordinates, we get : 



. Star 


Eight Ascension 


Declination 


a Canis Majoris 
a Canis Minoris 


35 46' 27" 
36 19 ; 42" 


-27 50' 28" 
-2 8' 48" 




In the above figure let A represent the position of the star 
Corn's Majoris when on the meridian at the latitude of Kuru- 
ksetra (30 N) in 4000 B.C. and B the position of the other star 
* Canis Minoris, NMS the eastern horizon. Join AB by an arc 
of a great circle and produce it to meet the horizon at M. Join 
B to P, the pole of the celestial equator, 



144 ANCIENT INDIAN CHRONOLOGY 

Now in the triangle ABP, the four consecutive parts are : 

/BAP, AP = 90 + 27 50' 28*,, L APB == 35' 15" 
andPB = 90 + 2 8' 48*. 

By solution of the triangle, the L BAP is found to be 1 16' 37" 
Now in the triangle ANM, we have 

AN = AP + 30 = 147 5V 28" 

Z MAN = 1 16' 37" and L MNA = a rt. angle. 

Now tan MN = sin AN. tan MAN. 
Therefore MN is found to be 40 7 47". 

There was thus not much azimuth error even at 4000 B.C. 
at Kuruksetra, if the observer took the great circle passing 
through the two stars as lying on the meridian, at the time of 
the transit of <x Canis Majoris. 

The mean date for the equality of the right ascensions 
of these stars being 4350 B.C., as shown before, we have 
thus shown that the date may as well be brought down 
to 4000 B.C. Equally strong reasons there may also be 
for raising the date by 350 years, tn., to 4700 B.C. Further 
the mythology as to Yama and his two dogs was perhaps the 
same for the Hindus, the Greeks and the Parsis. 

The Rg-Veda also speaks of the divine Vessel or boat in the 
following terms * ; 

" May we for our well-being ascend the well-oared, defectless, 
unyielding divine vessel, the safe-sheltering expansive heaven, 
exempt from evil, replete with happiness, exalted and right 
directing." (Wilson) 

The Atharva Veda also says : 

" A golden ship, of golden tackle, moved about in the sky ; 
there the gods won the Kustha, the flower of immortality." 2 

(Whitney) A.V. V, 4, 4 and VI, 95.2 



^foff 

\\\*\\ 

,63, 10. 



VEDIG ANTIQUITY 145 

"The well-oared ship of the gods, unleaking, may we, 
guiltless, embark in order to well-being." 1 

" A golden ship of golden tackle, moved about in the sky: 
there is tha sight of immortality ; thence was born the Kustha." 2 

(Whitney) 

Here the wish is, perhaps, that the departed souls going 
southward by the road guarded by the two dogs, a Ganis Minoris 
and a Ganis Majoris, may ascend the divine boat Argo-Navis 
and enjoy blissful expeditions in the heavenly river the milky 
^ay in the world of Yama. 

All these constellations viz., the two dogs and the Argo-Navis 
are to be found not only in the Vedas, but also in Greek and 
the Par&i Mythology. While in the Hindu literature these 
constellations were forgotten and called by other names, 
for example Ganis Majoris by Lubdhaka (the Hunter) and Canis 
Minoris by a star of the naksatra Punarvasu and the Argonavis 
is quite lost sight of in the later Hindu literature, the constella- 
tions are still used and so named in western astronomy. The 
names of the two dogs of Yama are preserved in the Zendavesta.* 
In the Parsi legend these two dogs 'keep the Kinvat Bridge* 
as imagined to have been made over the milky way. In the 
Greek legend the milky way is crossed by a ferry boat, $". e., the 
Argonavis. 

All these considerations lead us to think that the tradition 

, about Yama' s Dogs, belongs to the date of about 4700 B.C. and 

before the time when the Aryan peoples migrated to different 



Iff irrt ?8ftawnnft ^rere^n^r ft \\ 

A. V. VII, 6, 3. 



A. V. 19, 39. 7, 

3 Sacred Books of the Bast The Zend-Avesta, Vol. IV: pages 190, F. 
6 (14), pftge 213, F. XIX, 80 (98) ; also page 160, F. XIII. 9 (24), See also Intro- 
duction to the same, p. Ixxxvii 4, 

J9-1408B 



146 ANCIENT INDIAN CHEONOLOGY 

countries from their ancient homes. This ancient tradition in 
relation to the above constellations survived in the Vedas 
and with the western immigrants. These Aryan peoples probably 
lived near about the Central Asian mountain range running 
east west from the Mediterranean Sea to th Pacific Ocean. 
Here I have to difi'er from late Tilak v who in his book 'Orion', 
in the chapter on "the antelope's head," cites this tradition as 
a confirmation of his finding that the vernal equinox for the time 
was at the Antelope's Head* which according to him was the 
Mrga&ra's cluster. The tradition belongs to the pre-Vedic age, 
as I have shown before. 



CHAPTER XII 

VEDIC ANTIQUITY 
Legend of Prajapati and Roliini 

In the Aitareya Brdhmana l (iii, 36 or ch. 13, 9; the above 
legend is thus stated. We qoiote below the translation by 
Keith in his Rg-Veda Brdhmanas: 

" Prajapati felt love for his own daughter, the sky some say, 
Usds others. Having become a stag he 'approached her in the 
form of a deer (who had also become a deer). The gods saw 
him. * A deed unknown Prajapati now does.' They sought 
one to punish him ; they found him not among one another. 
The most dread forms they brought together in one place. 
Brought together they became this deity here ; therefore is his 
name containing (the word) Bhuta ; he prospers who knows 
thus his name. To him the gods said, ' Prajapati here hath done 
a deed unknown ; pierce him.' ' Be it so ' he replied, 'Let me 
choose a boon from you/ * Choose' (they said). He chose this 
boon, the over-lord-ship of cattle ; therefore does his name 
contain the word 'cattle.' Rich in cattle he becomes who teows 
thus this name of his. Having aimed at him, he pierced him ; 
being pierced he flew up upwards ; him they call 'the deer.' 
Tfie piercer of the deer is he of that name (Mrgavyddha) . The 



r ftf 



148 ANCIENT INDIAN CHKONOLOGV 

female deer is Eohinu The three pointed arrow i* the thre fc 
pointed arrow (trikanda). The seed of Prajapati outpoured ran ; 
it became a pond (Saras = a lake ?)." 

The Aitareya Brahmana passage is concluded by the aentenre 
"for the gods are lovers of mystery as it were/' We would 
add here that not only were the gods lovera of mystery but that 
their worshippers, the Vedic people were more so, If again 
Prajapati were a real person, we can only imagine how he would 
have treated those people who ware his worshippers and who 
indulged in such an obscene and vulgar allegory about himself. 

This legend has been noticed by Tilak in his Or/, S. 1J. 
Diksita in his Bharatiya, Jyotihdfttra, but the correct astronomical 
interpretation has not yet been found. Tilak and Diksita would 
understand that the astronomical phenomenon referred to in the 
passage indicates the time when the vernal equinox wan at the 
Mrgasii cluster or A, ^ and fa Orioni*. But our interpretation 
would be different. For the legend we have also to compare 
S. Br. I, 7, 4, 1 ; /it?. X, 61, 5-9," an Keith states. Another 
reference is Tandya JBr. 8, 2, 19. The Muhabhiirata A'tiM/d t'/vo 
parva> 18, 13-14, is another place where the pame legend it* ittated 
without any obscenity as found in the #0. !></</ and the Aittirt'yti 
Brahmana. It is possible, however, that the .]/, tth. legend IH 
later than the one recorded in the Vedic literature. The Vedic 
legetfi speaks of the birth of Budra, while the *U. tth legend 
refers to the ignoring by the godn of the share of iludra in a 
sacrifice. 

The phenomenon of Prajipati ineeiuig hi daughter (iohiiu 
is stated in the $g-Vcdu as tp luive happened in nud-hi*avn 
thus, 1 

" When the deed was done in mid-hcaw.n in the proxuuity 
of the father working his will, and the daughter coming together, 
they let the , seed fall slightly ; it was found upon the higU place 
of sacrifice/' (Wilson) 



VEDIC ANTIQUITY 



149 



The astronomical phenomenon was observed in mid-heaven 
or on the meridian of the observer. We have a star called 
Prajdpati in the Surya Siddhanta, viii ; 20, which is identified 
by Burgess in his translation, with 8 Aurigae, and his identifica- 
tion is faultless. We have also the Mrgavyadha (Sirius) of 
which another Vedic name was Svan (or the Dog), and Rohinl 
is of course the star Aldebaran. 

The legend divested of allegory is that the stars 8 Auriga 
and o- Tauri or Aldebaran were observed to cross the meridian 
almost together. This was understood by the gods as the most 
improper conduct on ^the part of Prajapati, and the god Eudra, 
then *born and stationed at the star Sirius pierced Prajapati 
(8 A urig a); his three-pointed arrow was most probably the line 
through 6, /3 and 8 Auriga, which have almost the same celestial 
longitude. Again the star Sirius, the three stars at Orion's belt 
and a Tauri or Aldebaran are very nearly in the same line. 
Here Eudra's three-pointed arrow may also mean this latter 
line through Orion & belt. The word ' trikdnda ' does not really 
mean three pointed, but perhaps having three joints, just as 
the joints are seen on a bamboo pole or in a sugar cane. If 
we take the latter meaning for the arrow of Kudra, it would 
not reach Prajapati or 8 Auriga, and Eudra would be a bad 
marksman, for piercing either Prajapati or Eoliini. 

We have thus to look for the time when Prajapati or 8 Auriga 
and a Tauri or Aldebaran had almost the same right ascension. 

In 1935 A.D. the celestial positions of these stars were as 
follows : 



Star 


Eight Ascension 


Declination 


8 Auriga 


5 ft 54^ !o-398 


54 16' 55'23N 


a Tauri 


4" 32'* 11 '248 


16 22' 48-63N 



and obliquity of the ecliptic = -23" 26' 5F'86. 



150 



INDIAN 



After transformation of the co-ordiaates, we have the following 
celestial longitudes and latitudes for the year 1935 A.D. : 



Star 


Celestial longitude 


Celestial latitude 


8 Auriga 
a Tauri 


89 (X By 
68 52' 50" 


+ 30 50' 21" 
-5 28' 1W 



The difference in their celestial longitudes was thus dO 7' 45* 
in 1935 A.D. In the following calculations the latitudes of the 
stars are supposed to remain constant throughout. 




In the above figure of the celestial sphere, lot ,T bo the polo of 
the ecliptic, PF the pith of the celestial polo round , R ami B 
the positions of the stars a Tauri and 8 Auriga respectively in the 
year 1935 A.D. 

(1) In the triangle ?rRB, the arc -R90-f 5 28' 19 ff , *B~ 
59 9' 39* and the angle EW3=20 7' 45* 

Hence the angle jrRB becomes = 26 4vJ> 47*. 

Now from * drav? ?rPQ perpendicular to the arc KB extended, 
then ffQ becomes - 26 34/ 54*. 

Thus there was or is no possibility of these two atar to have 
exactly the same right ascension at any past or future date, 
as TrP can never be equal to or greater than 26 34 ; 5i" 



VEDIC ANTIQUITY 



151 



We can thus determine only the time of their nearest 
approach to an equality of their right ascensions. 

At this time the position of the summer solstitial colure 
was the arc jrPQC. 

We readily find the angle En-Q = 92 44' 50" 

Hence tbe longitude of summer solstitial colure of the date in 
questipn was 92 44' 50* plus the celestial longitude of a Tauri 
for the ye&r 1935 A.D, 

This was thus 

= 92 44' 50" + 6.8 52' 50" 
= 161 37' 40* 

The shifting of the solstices thus was 71 37' 40" from which 
the number of years elapsed till 1935 becomes 5177 and the year 
or the date was thus 3243 B.C. in which the right ascension of 
a Tauri or Rohinl was almost equal to that of 8 Auriga or 
Prajdpati and the right ascensions of the two stars were 
also zero near* about the same time. 

The time Vhen 8 Auriga had its right ascension = 0, its 
longitude was 15 28' 40'', taking the valus of the obliquity 
of the ecliptic to be 24 5'. In 1935 the longitude of 8 Auriga 
was 89 0' 35'', so the increase in the celestial longitude of the 
star till 1935 A,D. = 73 31' 55'/, which represents a lapse of 
about 5829 years, or the year was about 3395 B.C. 

Similarly when the right ascension of a. Tauri was = 0, its 
longitude was = -2 27' V (- = 24 30 

Hence the increase in the celestial longitude of the star till 
1935 A.D. = 71 19' 5 1// representing a lapse of about 5167 years 
and the date was thus 3233 B.C. 

The above two dates, viz., 3395 B.C, and 3233 B.C. had 
between them an interval of 162 years. The right ascensions of 
these stars at these two dates are tabulated below : 



Stars 


R. A. in 3395 B.C. 


B. A. in 3233 B.C. 


8 Auriga 
a Tauri 


0' 0" ~ 
-2 0' 28" 


+ 2 2' 38" 
0' 0'' 



152 ANCIENT INDIAN CHRONOLOGY 

There are two more points in this connection which have 
to be considered : (1) The time determined, viz., 3243 B.C. 
being about the time when the equinoxial colure passed through 
the star a Tatm, the question now arises what had the Vedic 
Hindus to do with the position of the equinoctial colure in their 
sacrificial year ; and (2) why have we identified the star 8 Auriga 
of the 4th magnitude with Prajapati, or why we did not take 
a Auriga which is a star of the 1st magqitule and which is 
called Brahmahrdaya or the "heart of Brahma." 

With regard to the first point raised above we can say that 
the Vedic Hindus had a special sacrifice which was called 
Sydmdka Hgrayana the first millet harvest sacrifice which is 
thus described in the Kausltaki Brdhmana* IV, 12, 

" Next as to A gray ana. He who desires proper food should 
sacrifice with the Igrayana. In the rains 2 when the millet 
harvest has come, he gives orders to pluck millet. 

The new moon night which coincides with that time, on it 
should he sacrifice and then offer this sacrifice. * If he is a full- 
moon sacrificer, he should sacrifice with this and then offer the 
full-moon sacrifice. If again he desires a naksatra, he should 
in the first half of the month look out for a naksatra and offer 
under the naksatra which he desires." 

(Keith) 

We have not any interest in discussing the small inaccuracies 
which may be found in Keith* s translation; but we take 
that the rendering is substantially correct. The Sydmaka sasya 
or the millet is reaped in the month of Bhadra (lunar new-moon 
ending), which may begin from August, 19 to Sept. 15, and the 
full-moon of Bhadra oscillates between Sept. 2 and Oct. 1. It 
is thus quite possible for the full-moon of Bhadra to fall on the 



i vrf ^nrt 



3 The rains last for four months commencing from the day of summer solstice in 
.^orth India, 



VEDIC ANTIQUITY 153 

23rd of September as it did in the year 1934 A.D., it fell on 
Sept. 25 in 1923, on Sept. 22 in 1926. Hence the full-moon o 
Bhadra is, what is illustrated "as the Ha/rvesfc moon in astronomy 
and the SyamaJta Agrayanu, f nil-moon was such a Harvest Moon. 
This Agrayana fall-moon or the harvest moon is also mentioned 
in the Mahabhdrata* as the full-moon at the Krttikas (vide 
M. Bh., Vana. 82, 31-32 ; 82. 36-37 ; 84. 51-52 ; AnuSasana, 
25, 46). It appears that the Vedic Hindus had to use the 
autumnal equinoctial day in thair sacrificial calendar, and the 
autumnal equinoctial day is more in evidence than the vernal 
equinoctial day. 

It was on such" a full-moon night when the sun "was at the 
autumnal equinox, that the conjunction of Prajdpati and Rohinl 
(i.e. of 8 Auriga and a TCLIITI) by the almost simultaneous crossing 
of the meridian line was observed. The date as we have 
ascertained was about 3245 B.C. when the vernal equinox colure 
passed almost straight through the star a Tauri. Now-a-days a 
full-moon near the star Rohinl (Aldebaran) happens on the 2nd 
December, From the 23rd of September to the 2nd of Decem- 
ber the number of days =70, and at the rate of 74 years for the 
shifting of the equinoxes by one day, the time elapsed 
becomes 5180 years, the date becomes nearly the saare'15345 B.C. 
The astronomical phenomenon was that at the full-moon, 8 Auriga 
and a Tauri, almost simultaneously were observed to cross the 
meridian about the date found here at the place of the 
observe?, 

As to the second point why we have taken 8 Auriga, a star of 
the 4tH magnitude for Prajdpati, I would say that it is this 
star that is called so in the Stirya-Siddhanla 1 which has I trust 
faithfully brought down the tradition to our own times. Again 
8 Auriga represents the head of Ait,riga> and it was not improbable 
that this same const 3lla>tion used to be called Brahma in the 
Vedic literature. The star may no* be one of the fourth magni- 
tude, it was perhaps not so inconspicuous in those days, t?fe., in 
the third millennium B.C. If the whole solar system has been 
sweeping through space towards either the constellation Hercules 

1 Surya~SiddMnta, viii, 30. 
cj>0 1408B 



164 ANCIENT INDIAN CEBONOLOGY 

or Lyra, and the stars in the constellation Auriga being almost 
diametrically opposite have been steadily growing less and less 
bright. Hence 8 Auriga was not so inconspicuous before the third 
millennium B. C. The tradition preserved in the modern 
Sfirya-Siddhanta that Prajapati itself is the star 8 Auriga cannot 
thus be ignored, 

Again the star a Auriga is called in the Surya-Siddhdnta 
Brahmahrdaya or the "Heart of Brahma,' 9 and the Mahabharata 
legend tells us that " Eudra then pierced the heart of 
Yajna (Prajapati) with a dire (raudra) arrow, and Yajna (or the 
Sacrifice) fled therefrom in the form of a deer with Agni 
(ft Tauri ?). That Yajna (Sacrifice or Prajapati) in that form 
reached the heavens and shone there, being followed by Eudra." 1 
Here Rohini or Aldebaran does not coine in. We have to consider 
the case of the two stars which have ^almost the same celestial 
longitude ; and these were for 560 A.D. equal to 62 32/ and 
61 50' respectively of /5 Tauri and a Auriga ; their celestial 
latitudes were 6 22' N and 22 52' N. This is rather confusing, 
no astronomical interpretation is possible and the Mahabharata 
legend is quite unintelligible. The legend of Prajapati and 
Rohini astronomically interpreted does not yield the Y. Equinox 
at Mrgafiras** was suppbsad by Tilak in his Orion, pp. 20 et. seq. 

1 M. Bli. t Sauptika Parvan, 18, 13-14 : 



; \\ 



CHAPTER Xllf 

VEDIC ANTIQUITY 
Solstice Days in Vedio Literature and Yajurveda Antiquity 

In the present chapter it is proposed to extnine first if the 
Vedic Hindus knew of any method for determining the day of 
the winter or of his summer solstice, and secondly to interpret 
the various statements as to the solstice days as found in the 
Kausitaki Brahmana, the Yajurveda and the Mahdbharata and 
to settle the approximate dates in Vedic chronology as indicated 
by these statements. 

(I) The method of finding the solstice, days in Vedio 
Literature. 

The method of the Vedic Hindus for determining the solstice 
days is thus expressed in the following passage from the Aitareya 
Brahmana * : 



\ 

if 



Sayana has failed in his exposition of this passage which 
relates to observational astronomy, and no one who is unacquaint- 
ed with this branch of science can possibly bring out any sense 

1 Aitareya Brahmana, 18, lS t rjiuted by S. B. Diksita ia Ins 
p. 47. 



156 ANCIENT INDIAN CHRONOLOGY 

of it. We follow Keith generally with some modifications 
in the translation which is given below : 

' They perform the Ekavimsa day, the Visuvdn, in the middle 
of the year ; by this Ekavimsa day the gods raised up the sun 
towards the world of heaven (the highest region of the heavens, 
viz., the zenith). For this reason this sun (as raised up) is 
(called) Ekavimsa, Of this Ekavimsa sun (or the day), the ten 
days before are ordained for the hymns to be chanted during the 
day ; the ten days, after are also ordained in the same way ; in 
the middle lies the Ekavimsa established on both sides in the 
Viraj (a period of ten days). It is certainly established in the 
Virdj. Therefoie he going between (the two periods of 10 days) 
over these worlds, does not waver.' 

' The gods were afraid of this Aditya (the sun) falling from 
this world of heaven (the highest place in the heavens) ; him 
with three worlds (diurnal circles) of heaven (in the heavens) from 
below they propped up ; the Stomas are the three worlds of 
heaven (diurnal circles in the heavens) . They were also afraid 
of his -falling away upward ; him with three worlds of heaven 
(diurnal circles in the heavens) form above they propped up ; 
the Stomas are the three worlds of heaven (diurnal circles in 
the heavens) . indeed. Thus three below are the saptadasas 
^seventeen), three above ; in the middle is the Ekavimsa on 
both sides supported by Soarasdmans. Therefore he going 
between these Svarasdmans over these worlds does not waver.' 

The Vedic year-long sacrifices were begun in the earliest times 
on the 'day following the winter solstice. Hence the Visuvdn 
or the middle day of the year was the summer solstice day. 
The above passage shows that the sun 1 was observed by the Vedic 
Hindus to remain stationary, i.e., without any change in the 
meridian zenith distance for 21 days near the summer solstice. 
The argument was this that if the sun remained stationary for 21 
days, he must have had 10 days of northerly motion, 10 days of 
southerly motion, and the middle (eleventh) day *was certainly 
the day of the summer solstice ; hence the sun going over these 
worlds, in the interval between the two periods of 10 days on 
either side, did not * waver/ Thus from a rough observation, 



VEDIC ANTIQUITY 157 

the Vedic Hindu could find the real day of the summer or winter 
solstice. 

The next passage from the Aitareya Brdhmana (not quoted) 
divides the Virdj of 10 days thus : 10=6 + 1 + 3 ; the first 6 days 
were set apart for a Sadaha period, followed by an atirdtra or 
extra day and then came the three days of the three Stomas or 
Svarasamuns . The atirdtra days before and after the solstice 
day were respectively styled Abhijit and Visvajit days. It may 
thus be inferred that the Vedic Hindus by more accurate observa- 
tion found later on that the sun remained stationary at the 
summer solstice for 7 and not 21 days. 

Question may now be asked how could they observe that 
the sun remained stationary for 21 days and not for 23, 27, 29, 
or 31 days. This depended on the degree of accuracy of observa- 
tion possible for the Vedic Hindus by their methods of 
measurement. They probably observed the noon shadow of a 
vertical pole. 1 If we assume that the observation was made 
at the latitude of Euruksetra (about 30 N) and when the 
obliquity of the ecliptic was about 24 15', and the height of the 
pole was taken equal to, say, 6 ft., then : 

(a) When the sun had a longitude of 80, the length of the noon- 
shadow = 7*44 in. 

(b) When the sun had a longitude of 87, the length of the 
noon-shadow 6*98 in. 

(c) When the sun had a longitude of 90, the length of the noon- 
shadow =6*93 in. 

Now 7*44 in. - 6*93 in. = 0*51 in. and 6'98 in. - 6*93 in.~0'05 in. 

Hence by .using any sort of measuring rods, they could 
perhaps easily discern a change in the noon-shadow of about 
half an inch, but a difference of '05 in. was, of course, quite 
impossible of perception with them. They could thus infer that 
the sun remained stationary at the summer solstice for 7 days 
when they used any measuring rods and when they used rougher 

1 Another method possible for the Vedic people was to observe the sun's 
amplitude near about the 8. Solstice day, and this was found to remain stationary 
for 21 days. 



158 ANCIENT INDIAN CHRONOLOGY 

methods they could conclude that the sun remained stationary 
for 21 days at the summer solstice. 

At the winter solstice, the corresponding lengths of the noon- 
shadow would be 8 ft. 3 '46 in., 8 ft. 4'84 in. and 8 ft. 4'94 in. 
respectively. The changes in the length of the shadow were 
consequently 1*38 in. and O'lO in. respectively. 

It should thus be clear that the Vedic. Hindus knew how 
to determine the summer or the winter solstice day. When they 
found fcbat the sun apparently remained stationary at the solstice 
for 21 days, the true solstice day was the llth and when they 
found that the sun remained stationary for 7 days, they took 
the 4th day as the real solstice day. 1 

This finishes the first part of this chapter. We now pass 
on to consider how the Vedic Hindu stated his day of the winter 
solstice in successive ages. Some of these statements are 
the following : 

(a) The sun turned north on the new-moon of Magha ended. 

(b) ,, ,, ,, ,, ,, last quarter of Magha. 

(c) ,, ,, ,, ,, full-moon of Magha. 

(d) *> ,, ,, ,, one day before full-moon of Magha. 
(0) -, ,, ,, on the new-moon of Magha begun. 

1 The other metbod of determining the solstice day is described in Brliat SaMita 
of Varahamihira. Gbap. Ill, 3 : 



* The solstice day may he determined by observing the coincidence of the sun at 
the time of rising or setting with a distant sign-post; or by the marks of entrance or 
exit of the tip of the shadow of a gnomon in a large horizontal circle (having for its 
centre the foot of the gnomon)/ Here two methods are described by Varahamihira 
in the first of which the sun's amplitude at sunrise or sunset is to be observed. If the 
Vedic Hindus followed this method, they could perhaps observe the sun to remain 
stationary, i.e., without any appreciable change of amplitude, fur 21 days near the 
solstices. It does not appear probable that the second method was followed by the 
Yedic Hindus, In this connection the method followed by the Druids of the ancient 
Britons, with heir cromlechs (stone circles; as are seen in the Salisbury plains in Eng- 
land, for determining the solstice days may be compared. The first method described by 
Varihamihira readily led to the observation of the heliacal rising of stars in different 
seasons as has been found in the Vedas, 



VEDIO ANTIQUITY 159 

As wo shall see later on, these statements as to the day of 
the winter solstice occur in Vedic literature. The month of 
Mdgha (lunar) may begin now-a-days from the loth of January 
to the llth of February. What then is the meaning of this 
month of Mdgha as referred to in the above statements? Why 
should the sun's turning north be connected with a particular 
phase of the moon of such a movable month ? Unless and until 
we can answer the above questions satisfactorily, we cannot hope 
to interpret any of the above statements. 

We have very carefully considered the above questions and 
we may state our finding in the following" way : 

The Vedic Hindus did not have a sidereal reckoning of the 
year ; they followed a reckoning by lunar months of which 12 or 
13 formed the year ; in their reckoning the month of Mdgha, 
as it came every year, did not begin in the same part of the sidereal 
or the tropical year as it does not begin now also. If they had 
in use a sidereal calendar, they could state the solstice days by 
exact days of such a calendar. Unfortunately this they had not. 
They found out a particular lunar month of Mdgha (not occurring 
every year) to fix the beginning or the end of the five-yearly 
luni-solar Vedic cycle, and they stated the solstice days in 
reference to the phase of the moon of such a month of Mdgha. 
The winter solstice day was the beginning of the Vedio five-yearly 
cycles or Yugas and Sdmvatsara or year-long Vedic sacrifices 
were begun in the earliest times also from the day of the winter 
solstice* It is thus necessary for us to find the true meaning 
of this peculiar month of Mdgha : how it began and what were 
its characteristics. 

Meaning of the Month of Mdgha for Vedic Cycles 

As to the beginning of the month of Mdgha which was used 
for starting the Vedic five-yearly cycles the Jyantisa Vr.ddmgas 
(1400 B.C.) say : 



' When the sun, the moon and the Dhanisthds (Delphinis] 
Ascend the heaven together, it is the beginning of the Yuga (i.e., 



160 ANCIENT INDIAN OHBONOLOG-Y 

five-yearly Inni-solai cycle), of the month of Magha or Tapas 
of the light half and of the sun's northerly course. 9 Hence 
this month of Magha as used for starting the Vedic cycles must 
begin with the new-moon afc Delphinis. In the Jyautisa Vedaihga 
time the day of the very beginning of a such a Magha was the 
day of the winter solstice and thu^ it marked the beginning of 
the tropical month of Tapas, the first of winter, 

As to the time when the use of this month of Magha was 
accepted for making the Yedic calendar, we have the following 
passage from the Mahabharata : 



*MT I) 



* IT 



3 ^ ^ 



M. Bh., Vana, 230, 8-11. 

"Lady Abhijit (i.e., *Lyra), the younger sister of Rohini, 
being jealous of her, has gone to the forest to perform austerities 
with the desire of attaining the position of the elder. I arn 
thus confounded at this incident as one naksatra has been 
deflected from heavens. Hence Skanda, please find this time 
in consultation with Brahma/* Then Brahma fixed the time, 
beginning from the Dhanisthas, and Rohini (a Tauri or Aldebaran) 
became the first star. In this way the number of naksatras 
became proper (Sarnd). When Indra thus spoke to Skanda, 
the Krttikas flew to the heavens as the naksatra (star group) 
with seven heads, as it were, and it still shines as the one of 
which the presiding deity is Agni (Fire).' 

The passage quoted above shows that it was Brahma, a person 
of very high antiquity whose name was forgotten, who started 
the reckoning of time from the new-moon at the Delphinis, when 
Rohini beca-me the first star, and the Krttikds rose very probably 
exactly at the east. Here we have the time when the Ve^ic 



VEDIC ANTIQUITY 161 

five-yearly luni-solar cycles came to be started witb reference to 
the month of Mdgha. 

Now in Vedic literature Rohim means two stars, oiz. 9 Rohinl 
proper (Aldebaran) or Jyesthd (Antares). 1 For 1931 AJD. their 
longitudes were 68 49' and 248 48 ; according to our calculation. 2 
Hence these stars differ in longitude by almost 180 degrees, aad 
had respectively the longitudes of and 180 afc about 
3050 B.C. 3 

This was the approximate date when the month of Mdgha 
with its beginning with a new-moon at Delphinis was agreed 
upon as the standard month with reference to which the five- 
yearly Vedic luni-solar cycles were started and intercalary months 
loere determined. It was about this time that the number of 
na'ksatras (lunar mansions) was fixed at 27 by rejecting Abhijit 
(aLyra). It is here not necessary for us to attempt an explana- 
tion of the rivalry between either of the Rohinis and Abhijit. 

We have up to now settled that one feature of this standard 
month of Mdgha was that it should begin with B,' new-moon near 
the Delphinis. Another feature which follows from this is that 
it should have the full-moon near the star Maghd or Regulus, 
as the moon takes about 14*7 days, at the mean rate, to pass 
from /? Delphinis to a Leonis or Maghd. 

The third feature of this standard month of Mdgha was that 
at its last quarter (astakd), the moon should be conjoined with 
Jyesthd or Antdres as the Apastamba Grhya Sutra says: 4 



1 Taittiriya Samhita, 4, 4, 10. 

2 According to Burgess these stars had the celestial longitudes of 49 45' and 
229 44' in 560 A.D. Translation of the Surya Siddhanta, Calcutta University 
Reprint, p. 243. 

3 The conjunction of Aldebaran with the full-moon could perhaps only be 
observed by their simultaneous meridian passages on the equinoxial day in the Vedic 
times. The celestial pole of the time was very near to a, Draconis. The other possible 
method of observing the conjunction of the full-moon with Aldebaran on the equinoxial 
day was by joining the pole star with the moon and Aldebaran. In both th a se 
methods it was the B. A. which was really taken equal to Zero, and the elate for 
that comes out iib be 3233 B.C. 

4 Apastamba Grhya Sutra, viii, 81 1 19, 

21--I408B 



162 



ANCIENT INDIAN CHEONOLOGY 



* The VyastaM which comes after the full-moon at Magha 
(Regulus), has its eighth day (of the dark half) or last quarter 
with the moon at the star Jyesthd or Antares ; that is called 
Ekastaka.' 

The moon takes at the mean rate 7 '545 days or roughly a 
quarter of a synodic month to pass from Regulus to Antares. 

Thus we come to the conclusion that the Vedic standard 
month of Magha, in reference to which the Vedic five-yearly 
luni-solar cycles were started and winter .solstice days in 
successive ages were determined and stated, had three characters, 
viz., (1) New-moon at Delphinis, (2) Full-moon at Regulus, and 
(3) Last quarter at Antares. This month of Magha did not and 
also does not corue every year. We shall henceforth call thin 
month the Vedic Standard month of Magha. 

The Vedic Standard Month of Magha in Present Times 

We can now ascertain how and when such a standard Magha 
occurred or may occur in our own times. For 1931 A.D., 
/} Delphinis had a longitude of 315 23', a Lconis 148" 5'J', 
a Scorpionis or Antares 248 48' nearly. Hence this standard 
month of Magha should begin about the 5th February, should 
have the full-moon about the 18th February, and the last quarter 
about the 28th February, If we look for such a month coming 
in our own times, we had it as shown below : 



Year 


Begin sing 


Full-moon 


Lat, quarter 


Now-moon 


1924 


Feb. 5 


I?cb. go 


Feb. 27 


Mar. tf 






i 






1927 


Feb 2 


! Feb. I 


Feb. 24 


Mar. a 


1932 


Feb. fi 


| Feb* 22 


Fob. 2ft 


Mar. 7 


1935 


Feb. 


i Feb. IB 


Feb. 26 


Mat, 5 



The Vedic standard month of Magha is thus noi strictly 
unique in its position in the sidereal year. All points considered 
we are inclined to take that this Magha happened in our time 
in 1924 A.D. from the 5th February till the 5th March. This 
year and this month we shall use as our gauge year and month 



. VEDIG ANTIQUITY 168 

in interpreting the different statements of the days of the 
winter solstice as occurring in Vedic literature. 1 

(ii) Statements of Solstice Days in Vedic Literature 

We are now going to state and explain the references 
from the Brdhmanas and other works which -either directly state 
or indicate the winter solstice day of the successive Vedic 
periods. 

(A) The first reference is from the Kausltaki Brdhmana, and 
it was first found by Weber : 



tH 1 t** 



ST Hu*u^ij<^5v{wil few 



ci 



This passage has thus been translated by Keith in his Rg-Veda 
Brdhmanas : 

' On the new-moon of Mag ha he rests, being about io turn 
northwards; these also rest, being about to sacrifice with the 
introductory atimtra ; thus for the first time they obtain him ; 
on him they lay hold with the caturtiimsa ; that is why the 

1 The year 1924 A.D. is aiso similar to the year 80 A. D. of whicb the lab day of 
MagUa was the epoch of the Paitamaha Siddhanta of the PancasiddhantiM of 
\ 7 'arahamibira. The interval of 1844 sidereal years =673532 -73 da and 22808 lunations 
=673533 65 da. The difference is only about a day, 

2 Kau^taki Brahmaya, xix, 3. 



164 ANCIENT INDIAN CHfiONOLOGi* 

laying hold has its name. He goes north for six months ; him 
they follow with six-day periods in forward arrangement. Having 
gone for six months he stands still, being about to turn south- 
wards ; these also rest, being about to sacrifice with the Visuvant 
day ; thus for the second time they obtain him. He goes south 
for six months ; they follow him with six-day periods in reverse 
order. Having gone south for six months he stands still, and 
they about to sacrifice with the Mahavrata day obtain him for 
the third time. In that they obtain him thrice, the year is in 
three ways arranged. Verily it serves to obtain the year. With 
regard to this, this sacrificial verse is sung, 

Ordaining the days and nights, 
Lite a cunning spider, 
For six months south constantly, 
For six north the sun goeih. 

For six months he goes north, six south. They should not 
consecrate themselves at this time ; the corn has not arrived, 
the days are short, shivering they come out from the final bath 
(avabhrtha) . Therefore they should not consecrate themselves 
at this time. They should consecrate themselves one day after 
the new-moon of Gaitra ; the corn has come, the days are long, 
not shivering they come out from the final bath. Therefore that 
is the rule'. 

Here it is definitely skated that on the the new-moon of Mdgha 
the sun reached the winter solstice. 1 This new-moon is without 
any doubt that new-moon with which Mdgha ended. The 
definition or meaning of this month of Magha has been found 
before. This statement shows that the 5th of March, 1924 A.D., 
was the; true anniversary of this determination of the winter 
solstice. Now on the 5th March, 1924, G. M. noon, the sun's 
mean longitude was 

= 342 57' 46" 

= 842 58' to the nearest minute. 

This longitude was near to 270 in the year of this determina- 
tion of the solstice day. It shows a shifting of the solstices by 

1 This is perhaps the oldest tradition of the solstice day as recorded in this 
Brahmaiia. 



\ElXLC AiSTlQUriY iG5 

about 72 58', representing a lapse of about 5,268 years, till 1924 
A D. But we have yet to allow for the sun's equation. Now 
in 52*44 centuries before 1900 A.D., the longitude of the 
sun's apogee was = 11 30' nearly and the eccentricity of the 
solar orbit was about '018951. Hence the sun's equation for the 
mean longitude of 270 was, + 2 8' nearly. 

This equation of *- 2 S' is now applied to the mean longitude 
of the sun on the 5th March, 1924, at G. M. noon, viz., 342 58 f . 
The result obtained, viz., 345 6 ; , was equal to 270 in the year 
of this determination of the winter solstice day. Hence the total 
shifting of the solstices becomes 75 6' nearly ; this indicates a 
lapse of 5,444 years till 1924 A.D., or the date of this determina- 
tion of the solstice becomes near to 3521 B.C. Now as we want the 
year similar to 1924 A.D. as regards the moon's phases in relation 
to the fixed stars, the date arrived at requires a little adjustment. 
We have already obtained 1 the luni-solar cycles of 8, 19, 160, 
1939, etc., years in which the moon's phases near to fixed stars 
repeat themselves. ' 

Now 5444 = (1939 x 2 + 160 x 9 + 19 x 6 + 8) + 4 . Hence elapsed 
years must now be taken as 5440 from which the required year 
* comes out to be 3517 B.C. 

The sun then turned north in 3517 B.C. on the new-moon 

day of Magha and the first year of the luni-solar cycle commenced 

from the said new-moon day. The question now is, ' how could 

they find the next winter solstice day.' They counted full 366 days 

or 12 months and 12 nights after which they estimated that the 

sun would reach the winter solstice. This sort of reckoning 

continued till the five-yearly cycle of 62 lunar months was 

exhausted. They then thought that the same type of Magha 

returned, or they might check their reckoning in 3, 5, 8, 11 or 

19 years by actual observation. Hence their predicted day of 

the winter solstice, when not checked by actual observation, was 

almost always in error, but perhaps was still within their limit of 

21 days Their observed solstice days, however, were always correct. 

It may be asked how the Vedic year came to have 366 days 

or 12 lunar months + 32 nights. Generally this year is stated 

1 Chapter 1, p. 27. 



166 ANCIENT INDIAN CHKONOLOOY 

in. many places to consist of 360 days only. How is. this 
discrepancy to be explained ? In a half year there were .the 
ordinary 180 days + 2 atirdtra days, then came the Visuvdn, 
the middle day of the year which belonged to neither half 
and then came the other half with 180 days +. 2 atirdtra days and 
lastly came the Mahdvrata day. In all, therefore, there were 
in the year 2(180 + 2) +2 or 366 days. Of the two atirdtras 
of the northerly course, the first was the Prdyanlya and the 
second the Abhijit day. Similarly in the sun's southerly course, 
the first atirdtra day was the Visvajit day and the other had a 
suitable name. The Vedic ytar had thus 366 days or 12 lunations 
+ 12 'nights.' x 

One point more we want to settle is that when the Vedic 
year was taken to begin. The answer is now easy. The 
Vedic year normally began on the day following the winter 
solstice, and winter then began and lasted for two months. 
Winter .was thus the first season of the year. There was next 
felt the difficulty of beginning the year- long sacrifices with the 
winter solstice day, as the time was unsuitable on the ground 
of its being extremely cold, as it was the non-harvesting time and 
as the days were then very short. Then rule was made to" 
begin these sacrifices, not from the winter solstice day but full 
two months and one day or exactly 60 days later, when Spring 
set in, or as the text says, ' One day after the nfew moon of 
Caitra. Thus the first season, though winter formerly, became 
spring in later reckoning (sacrificial year) and winter then became 
the last season of the year. 

We have found out the year when the sun turned north on 
the new-moon'of Mdgha to have been 3517 B.C. by taking the 
standard month of Mdgha as the one which happened from the 
oth of February till the 5th of March, 1924 A. D. Our date is 



Of. 

Jyautisa t 28. 



" A year is three hundred with sixty six of days. Tn it there are five seasons and 
two courses (of the sun)." 

In this connection it should be remembered that the atiratra days were not 
reckoned in the sacrificial calendar, 



VEDIC ANTIQUITY 167 

perhaps liable to shifting of about one or two centuries either 
way if we took the gauge year to be 1927 or 1932 A.D. This 
amount of possible shifting must be considered negligible at such 
a remote age. It is perhaps needless to point out that unless we 
can find out a correct interpretation of passages like above, no 
determination of time would be possible. 

A question may yet be raised, if of the phrase ' the new- 
moon of Mdgha, 9 the word Mdgha means the full-moon ending 
month of Mdgha. Our answer is that we have taken the month 
of Mdgha as the new-moon ending not without any reason. In the 
Jyautisa Veddmgas we get the new-moon ending months alone ; 
not a single verse in them can be interpreted to mean the full- 
moon ending months. In the case of the new-moon ending 
Magha, we have established three distinctive peculiarities as 
already pointed out and that such a month of Mdgha was 
associated with ihe winter solstice day and the starting of the 
Vedic five-yearly cycle or Yuga. The word Mdgha as used in 
connection with the solstice days must have a definite meaning, 
7*. e., must mean more or less a unique synodic month not occurring 
every year. As to the full-moon ending Mdyha, we have not yet 
discovered any unique meaning either from the Jyautisa Veddmgas 
or from other Vedic literature. Thus while we are so much 
in doubt as to the characters of a unique full-moon ending month 
of Mdgha, the characters of the new-moon ending Mdgha are 
very clear and well-pronounced. We thus consider it fruitless 
to speculate upon the characters of a Vedic full-moon ending 
unique Mdgha to interpret the references like the above. 1 We 
now pass on to our next reference. 

(B) This reference was quoted by Tilak in his * Orion ' on 
pp. 44-45 and runs as follows 2 : 



3* 



^rfo* 



1 Further the fnll-moon ending Magha cannot include the Ekastaku d&y as defined 
before. This is a serious defect of the full-moon ending months. 
a Taittiriya Samhita, VII, 4, S, also Tdndya Bralimana, V, 0. 



168 ANCIENT INDIAN CHRONOLOGY 



**: 



This passage is from the T ait tiny a Samhita. The Tandya 
BraJimana bas also almost the same passage with slight altera- 
tions as may be seen from Tilak's quotation in his ' Orion. 9 We 
translate the above passage following him generally thus : 

* Those who want to consecrate - themselves for the yearly 
(year-long)" sacrifice should do so OQ the Ekdstakd day. This 
is the wife of the year what is called Ekdstakd and he, the 
year, lives ID her for this night. Those that consecrate on the 
Ekdstakd truly do so in a distressed condition, as it is the season 
(winter) which is reckoned the last of the year. Thus those 
that consecrate on the Ekdstakd do so in the reversed order 
as it marks the last season of the year. They should 
consecrate on the full-moon at the Phalgus as it is the mouth 
of the year. They thus begin the yearly (year-long; sacrifices 
from the very mouth ; but it has one defect that the Visuvdn 
(the middle day of the year) falls in the rainy season. They 
should consecrate themselves at the full-moon near Citrd 
\Spica or a Virginis), as it is the beginning of the year. They 
thus begin the sacrifice from the very mouth of the year. 
Of this time there is no fault whatsoever. They should consecrate 
themselves four days before the full-moon (near Citra). Their 
Kraya (i.e., purchase of Soma) falls on the Ekdstakd (here the 
last quarter of Caitra). Thereby they do not render the Ekdstakd 
void (i.e*, of no consequence)). Their Sutyd (i.e., extraction of 
Soma juice) falls in the first (light) half of the month. Their 
months (monthly sacrifices) fall in the first half. They rise 
(finish) in the first half. On their rising, herbs and plants rise 
after them. After them rises the good fame that these sacrifices 
have prospered. Thereon all piosper/ 



VEDIC ANTIQUITY 169 

The Taittiriya Samhitd here records three days of the winter 
solstice, the first two of which were traditional and the last 
one most likely belonged to the date of this book. These 
are: 

(1) The Day of Ekastaka. 

(2) The Day of the full-moon at the Phalgus. 

(3) The Day preceding the full-inoon of Magha. 

As in the Kausltaki Brdhmana here is expressed a dislike 
for beginning the yearly sacrifices with the beginning of winter. 
Some centuries later than the tradition recorded in the 
Kausltaki Brdhmana, it was observed that the winter solstice 
had preceded by nearly 8 days and fell on the Ekdstakd day, i.e., 
on the day. of the last quarter, of the Standard month of Mdglia 
on which the moon was conjoined with Antares. This day 
corresponded with the 27th February of 1924 A J>. of our time. 
Hence the date for this position of the winter solstice as obtained 
by observation comes out to have been 2934 B.C. 

It was about this time taken as a rule that the year-long sacri^ 
fices should be begun from the day of Ekdstakd.^ But as this 
was the beginning of winter, it was considered unsuitable for the 
purpose chiefly owing to the extreme cold nature of the. season 
which made the sacrificer shiver on coming out of the water 
after the bath of avabhrtha. People then came to think that 
the yearly sacrifices should be begun according to an older tradi- 
tion, fc., that the day of the full-moon night near the Phalgus 
was the first day of the year. This day had been the day 
of the winter solstice many centuries before the time. The 
time when this was the position of the solstices was about 
4550 B We cannot be sure if at this high antiquity there 
was anything like the standard month of Mdglia agreed upon. 

i The Puna MAnMffl, quotes the following traditional days for the Gavamayana 



The ^nnnentator Savara quotes the Toft** * ** * T ^* **** 

for elucidation. 

23 lAOflfc 



170 ANCIENT INDIAN CHRONOLOGY 

But the sacrifices who thought that "the EMstaka "day was 
unsuitable 'for beginning the yearly sacrifices, calculated that 
the full-moon at the Phalgus would happen |tH of a month 
or 22 days later, and that the middle day of the year wduld 
happen 22 days after the sun crossed the summer solstice a day 
which was almost at the middle of the rainy season* Hence if 
they began the yearly (year-long) sacrifices at the beginning of 
spring i.e., full two solar months or two lunar (synodic) months 
plus one day later, the Visuvdn or the middle day of the sacrificial 
year would be the first day of autumn and there would be 
no inconvenience due to rainy weather on that, day. 

When the -sun reached the winter solstice on the day of the 
last quarter of the standard month of Magha, spring would begin 
full two synodic months plus one day later ; consequently th? 
day most suitable for beginning the yearly sacrifices would be 
the day following the Caitri EMstaka or the last quarter of 
Caitra. In its place the Taittinya Samhita recommends tbat 
yearly (year-long) sacrifices should be begun from the full-moon 
day of Gaitra or Gitrd Paurnamasi day. This being the beginning 
of spring, the winter solstice day was one day -before the 
full-moon day of the standard month of Magha. 

This full-moon day of Magha corresponded with the 20th 
February, 1924 A.D., and the year in which the winter solstice 
day fell- on the full-moon day of Magha was 2454 B.C. 1 The 
time indicated by the rule of the Taittinya Samhita 'becomes 
about 2446 B.C. Judged by this latest tradition recorded in it, 
the date of the Taittinya Samhita should be about 2446 B.C. 
The other two traditions which it contains were true for about 
4550 B.C. and 2934 B.C. respectively, of which the former, is of 
doubtful value. 

(c) In the Mahabharata. there are several passages which 
directly or indirectly indicate that the nights of the full moons at 
the KrttiMs and the Maghas, were respectively the a'utumnal 

* ' * Eight yars after 2454 B.C., the full moon of Magha fell one day later, than the 
Viator splstice day. Incur 6nding this year^tz., 2446 B.C was the year in which 
Yudhiftbira began the Afoamed'bQ sacrifice. This has beep fufly discussed o& 
page 32. 



VEDIC ANTIQUITY 17i 

equinox and the winter solstice days and thus particularly 
auspicious for the performance of some religious observances : 



(i) - 



'The man who goes to Puskara specially at the full-moon 
at the Krttikas, gets the blessed worlds for all times at the 
house of Brahma.' 



(2) 



' A person reaching a holy bathing place at full-moons at the 
Krttikas (Pleiades) and the MagMs (Regulus), etc. gets the 
merit of having performed respectively the Agnisioftia and ^the 
AtirStra sacrifices/ " - ' ' 

Here it is significant -that the difference in celestial longitudes 
of Pleiades and Regulus is very nearly equal to 90 degrees. 



(3) ^laNti^taiPi M^fs ^e-itci^mi I 



* At Prayaga (the confluence of the Ganges and the Jamuna) 
at the full-moon at the Maghas, three crores and ten thousand 
holy waters meet/ 



(4) 

U 



' On the full-moon at Krttikas, if a man should go to the 
bathing place called TTrvafi and bathe in the Lauhitya (the river 
Brahmaputra), according to Sastric rules with a devoted or 
prayerful mind,- he would get the religious merit of having per- 
formed the PunAanka sacrifice/ 

1 M. Bh.j Vana, 82, 31-32. 
8 M. Bh., Vana, 84, $1-52. 
3 M. Bh., Anutasana, 25, 35-36. 
M. Bh., Anutasana, 25, 46. 



ANCIENT INDIAN CHBONOLOGY 

We have already ascertained the time when the fall-moon 
day of the standard month of Magha was also the winter solstice 
day ; it was the the year 2454 B.C. 1 The Mahabharata 
references quoted above show that the old observers could 
ascertain that at this time the vernal equinox was near to the 
Krttikas (Pleiades) and the summer solstice at the MagMs (or 
near to the star Regulus). This position of the equinoxes and the 
solstices was perhaps regarded as correct till up to 2350 B.C. 

*> 

(D) We now come to a different sort of statement, not 
connected with the month of Magha , from the Brdhmanas as to 
the beginning of the year expressed in terms* of the fullness of 
the moon near to the Phalgus : 



" Next as to the four-monthly sacrifices . He who prepares 
for the four-monthly sacrifices, begins on the full-moon 
night of the Phalgunls. The full-moon night of the Phalgunls 
is the beginning of the year ; the latter two (uttare) Phalgus 
are the beginning and the former two (Purve) the end (i.e., 
puccha or the tail). Just as the two ends of what is round (viz. , 
the circle) may unite, so these two ends of the year are 
connected/ (Keith) 

We proceed to find the time indicated by the above passage 
on the hypothesis that this reference states the day of winter 
solstice and not the beginning o spring. 

Winter Solstitial Point and Deduced Date 

We have now to settle the exact indication of the winter 
solsticial point from the above Brdhmanas reference. The fuli- 
moon at the Purva Phalgus was the last night of the year, while 
the full-moon at the Uttara Phalgus the first night of the next 

1 Chapter II f Mahabharata, Kaliyuga t pp. 40-42. 

2 Kausitaki Brahmaqa, 5, 1. 



VBDIC ANTIQUITY 173 

year. If we take the meaning that the sun reached the winter 
solstice at the full-moon at the Purva Phalgus, from such 
references, we arrive at the year 3293 B.C. On the other hand, 
if we take that the sun in opposition to ft Leonis marked the 
winter solstice, the date comes out to be 3980 B.C. Here is 
produced a difference of about 700 years. 

Now, the Vcdic full-moon nights were not one but two in a 
lunar month, the first of which was the Anumati Paurnamdsl and 
the second was the Rdkd Paurnamdsi. 1 These two full-moon 
nights were consecutive. Hence we should take the full-moon 
occurring somewhere midway between the stars and ft Leonis 
as indicative of the winter solstice day of this Brdhmana period. 

Now the celestial longitude of B Leonis for 1931 A.D. 

=162 24' 
and the celestial longitude of (3 Leonis for 1931 A.D. 

= 170 41' 

.'. The mean of the longitudes of these stars for 1931 A.D. 

= 166 32' 

Now on the 6th March, 1928, a full-moon happened at 
12 hrs. 34 mio. Gr. M. T. and the sun at G. M. noon had the 
longitude of 345 40 r nearly. From which the total shifting of 
the solstices becomes 75 40' as a first approximation. The date 
comes out to be about 3550 B.C., which we understand to be 
earliest date for the inception of Brdhmana literature as deduced 
from the above statement. 

If the full-moon day of Phdlguna be distinctly indicated as 
the beginning of Indian spring, in any of the Brdhmanas, the 
work in question must belong to a date of which the superior 
limit would go down to about 625 B.C. as will be set forth 
later on. 

Conclusion 

We have thus shown from the direct statements as found 
in the Brdhmanas, that the beginning of this class of literature 
and of the religious ceremonies prescribed in them began from 

1 Aitareye Brahma^a t xxvii, 11, etc. 



174 



ANCIENT INDIAN CSBONOLOGt 



about 3560 B.C. The actual dates arrived at are tabulated! 
below : 



Date arrived at 
(approximate) 


Eeference or basis 
of date 


Gauge year and date 
correct to W. S. Day 


3550 B.C. 


ID) 


1928 A.D. 6th March 


3517 B.C. 


(A) 


1924 A.D. 5th March 


2934 B.C. 


(B) 


27th Feb. 


2454 B.C. I 
to 
2350 B.C. J 


(C) 


,. ., 20th Feb. 



The above dates indicated in the Brahmaiias, cannot be all 
classed as mere traditions. The year of the Bbarata battle falls 
within this range and was the year 2449 B.C. as has been 
established in Chapters I-III. 

As to ,the references . which use the month of Magha for 
stating the solstice days, the gauge year could as well be 1927 
A.D., and we cannot. say if the Vedic Hindus did not sometimes 
use tbe type of Magha which happened this year. This would 
tend to lower some of the dates as connected with Magha by 
about 200 years. The reference (A) would indicate the date 
3308 B.C. nearly ' when Rohini became the first star/ 1 

This chapter is divided into two parts, in the first of which 
we have shown that the Vedic Hindus knew of a method of 
finding the solstice day of either description of any year. In 
the second half we have established that there was a standard 
month of Magha in their statements of the solstice days in 
successive ages, and we have found out a set of dates extending 
from 3550 B.C. to 2350 B.C. during which some sort of Sanskrit 
literature known as the Brdhmanas began to be formed. 



. Blu, Vana, 230, 841, quoted before. - 



CHAPTER XIT 

BKIHMANA CHBONOLOGY 

Solar Eclipse in the Tdndya Brdhmnna 

Asnoticed by late Sankara Balakrsna Diksita, in .his 

page 63 (1st. edn.), there are references to solar 



eclipses in five places in the Tdndya Brdhmana which are (1) 
IV, 5, 2 ; (2) IV, 6, 13 ; (3) VI, 6, 8 ; <4; XIV, 11, 1445, 
and (5; xxiii, 16, 2. In all these leferences it is stated that 
Svarbhdnu struck the sun with darkness, Of these five references, 
in the two, viz., VI, 6, 8 and XIV, 11, 14-15, it is said that it 
was Atri who destroyed the darkness from the front of the sun ; 
in the remaining three references the removal of darkness from 
the sun is ascribed to the Devas or gx>ds. Diksita "would take 
the word 'Devas' to 'mean the ""sun's rays." Whatever" 
the meaning of the word 'Dems 9 may be, it is clear that the 
references which speak of Atri as the person who dispelled the 
darkness that lay on the sun's disc, speak of the solar eclipse 
as described in the Rg~Veda, V, 40, the time of which 
has been already ascertained in Chapter IX as the 26th July, 
3928 B.C. It is proposed in the present chapter to determine 
the date of this another eclipse of the sun as mentioned in the 
Tandy a* Brahmana, and understood as such by Diksita, He had 
also found a reference to a solar eclipse in the tfatapatha 
Brahmana, V, 3, 2, 2 and which has been often quoted by sub- 
sequent writers. The three references of the Tdndya Brdhmana 
as to this special eclipse are the following : 



(a) " 



T. Br. IV, 5, 2. 
0>) 



176 ANCIENT INDIAN CHRONOLOGY 



T. Br., IV, 6. 13. 
(c) 



T. J3r., XXm. 16, 12. 

These passages may be translated as follows : 

(a) " Svarbhanu born of Asura, struck the sun with darkness, 
which was dispelled by the gods with Svaras (hymns) ; hence the 
Svarasdmans are for the rescue of the sun " 

(b) " Svarbhanu, the Asura, struck the sun with darkness. 
The gods removed this darkness by singing the Divakirtya songs 
(i.e., songs sung during the day time). Whatever are known as 
Dwakwtyas, are (the agents) for the destruction of darkness. 
These Divdklrtya songs are the rays of the sun. By the rays 
alone the snn is truly begun/' 

(c) " Svarbhanu, the Asura, struck the sun with darkness ; 
for this the gods wanted to purify him and they got these 
Svarasdmans I by these they removed the darkness from the sun." 

These passages all indicate that the solar eclipse in question 
happened on the Visuvant day, which means according to the 
Taittiriya Samhitd as " the middle day of the sacrificial year 
begun from spring. " It meant the day on which the Indian 
rains ended and the Indian autumn began. To be more precise, it 
meant the day on which the sun's tropical longitude became 150. 
According to the Vedic sacrificial calendar, there were the three 
Sv&rasarn&n days before the Visuvant, and three Svarasdman 
days after the Viwwmt. On these seven days (including the 
Visuoant) the Divakirtya songs were sung. We thus infer that 
the solar eclipse happened on the Visuvant day, i. e., on the day 
on which the sun's tropical longitude was about 150 degrees. 

What is here said in the Tdndya Brahmana about such a 
peculiar solar eclipse "happening on the Visuvant day, must be a 
tradition of a past event only. By exploring the period from 
2553 A I), to -1296 A-P- with the help of the eclipse cycles 



BEAHMANA CHRONOLOGY 177 

deduced in Chapter IX on the " Solar Eclipse in the Rgveda, 
we find after a few trials that a solar eclipse took place in the year 
-2450 A JX on Sept. 14, on which at GK M. T. 6 hrs or 
Kuruksetra Mean Time 11-8 A.M., the lunisolar elements were : 

Mean Sun = 152 12' 22"*35 
,, Moon = 148 32 16*30 
Lunar Perigee == 102 50 30*85 
A. Node = 143 51 1'82 

Sun's apogee = 27 1 51'86 
Sun's eccentricity = 0*018331. 

The full calculations of the circumstances of this solar eclipse 
are set forth in the Appendix, We briefly summarise them for 
the station Kuruksetra, : 

Date : September, 14, -2450 A.D. (i.e., 2451 B.C.) 

Longitude of conjunction of Sun and Moon = 150 18' nearly 

Time of beginning of the solar eclipse = 5-27 A.M., K.M.T. 
,, ending z , ,, = 7-4 ,, ,, 

, , ,, nearest approach of centres = 6-4 ,, , 

Magnitude of the eclipse = 0*41 = 5 Indian units 

Duration of eclipse = 1 hr. 37 m. 

Time of Sunrise = 5-32 A.M., K.M, Time. 

The eclipse began almost with the sunrise. 

We have carefully examined the period from 2554 B.C. to 1297 
B.C. and are satisfied that no other solar eclipse happened in this 
period with the sun's longitude at 150 nearly and which was 
visible at Kuruksetra. 

The Tdndya Brdhmana therefore records the solar eclipse on 
the Visuva\t day in its references in IV, 5, 2 ; IV, 6, 13 and 
XXIII, 16, 12. It is not unlikely that the Satapatha Brdhmana 
also in V, 3, 2, 2 records the same traditional eclipse. We can 
not, however, by this finding settle if the Tdndya Brdhmana is 
to be dated earlier than the Satapatha Brdhmana. It will be 
shown later on that the Jaiminlya Brdhmana and the Tdndya 
Brdhmana indicate a common date of about 1600 B.C. 

23 1408B 



178 ANCIENT INDIAN CHEONOLOGY 

APPENDIX 

Calculation o/ the Solar eclipse mentioned in the 
Tdndya Brahmana 

Date September, 142450 A.D. (2451 B.C.) 

Julian day No. 826452. 
Epoch : 6 A.M., G.M.T., i.e., Kuruksetra Mean Time 

11-8 A.M. 

(i.e., 43*49 J. C. and 97 days before Jan. 1., 1900, G% M. 
Noon.) 

Mean Luni-solar elements 

Mean Sun = 152 12' 22"*35 
Mean Moon = 148 32 16'80 
L. Perigee = 102 50 30'85 
A. Node = 143 51 1'82 

Sun's apogee = 27 1 51*86 
Solar eccentricity - 0'018331 

Let A represent the epoch hr. midnight Gr. M. T. or 5-8 A.M. 

Kuruksetra time 
B ,, 2 A.M.,G.M.T. or 7-8 

^ >? ^ ?> > V'O ,| ,, 

Mean Sun Mean Moon 

At A = 151 57' 35"'28 At A = 145 14' 37"'54 

B = 152 2 30-97 B = 146 20 30'46 

152 7 26'66 ,, C 147 26 23'38 

Moon's Perigee 

At A = 102 48' 50^*59 
B = 102 49 24'01 
= 102 49 57'43 

Sun's apogee = 27 1' 51'86 

A. Node 

At A = 143 51' 48^*96 

B - 143 51 33-08 

,, = 143 51 17'20 
Sun's eccentricity (e) = 0*018331 
(2) radians ** 125 /4 745 [2'0994901] 
(fe) radians ==_ 1''487 [Q-1575563] 



BBIHMAETA CHRONOLOGY 
Longitude of Sun 

At A At B 

Mean Sun = 151 57' 35 152 2' 31" 

Total equation = -1 4426 -1 4420 
Apparent Sun = 150 13' 9" 150 l& 11" 

Longitude of Moon 



179 



At C 

152 7' 27" 
-1 44 14 
150 23' 13" 





At A 


At B 


At G 


Mean Moon = 

Total of six prin- I .... 
cipal equations J 

Moon on orbit = 


145 14 38 
4-3 20 30 
148 35 8 


146 20 30 
+ 8 27 55 
149 48 25 


147 26 23 
'+3 35 14 
151 1 37 


A. Node (0) 


143 51 49 


143 51 33 


143 51 17 


F X -M-0 


4 48' 19* 


5 56' 52* 


7 10' 20* 


2Fi = 


9 26' 88* 


11 53 44 


14 20 40 


Seduction = 


1' 8* 


1' 26 


1' 43* 


App. Moon = 


148 34' 0" 


149 46' 59* 


150 59' 54* 



Instant of New moon ^ 8-3 Kuruksetra Mean Time. 
Latitude of Moon 



+ 528-3 sin 

-25*0 sin (Fi-gO = 
+23'8sin(F 1 + gO = 
+23'2sin (F 1 -g) - 

-23'6sin(F 1 -2g) = 
+ 22-1 sin (F 1 +2D\ 



+ 1518-"2 


+ 1918'"9 


-105-1 


-95-5 


-21-6 


-21-9 


-18-3 


-18-0 


-14-2 


-14M 


+23-2 


+ 23-3 


+ 15-2 


+ 15-5 



Total = +1397-4 
Latitude = +23' 17" '4 



+2312-"! 
-86-0 
-22-1 
-17-6 
-14-1 
+23'4 
+ 15-8 
+ 1808-2 +2211-5 
+ 3(X8"-2 +36'51"'5 



180 ANCIENT INDIAN CHRONOLOGY 

Moon's Horizontal Parallax 

P = 3422'"7+ 186*6 cosg + 34*3 cos (2D-g) + 28'3 cos 2D 

For 'B' 

+ 186'6 cosg = + 185*'8 

+ 34-3 cos (2D-g) = +19-7 

+ 28'3 cos 2D = 17*7 

Const. = 8422-7 



3605"'4 = 60' 5" '4 H. Parallax. 

Moon's semi-diameter = 16' 22" *4 
Sun's = 17' 10"'9 
Sun's Horizontal Parallax = 8"*9 

Calculation of the Eclipse for Kuruksetra 
( Long. = 5* 8 W East, and Lat. = 30 N) 

A B ' c 

R. A. of Mean Sun = 151 57' 35" 152 2' 31" 152 7' 27" 
Local mean time 
(from 12 noon) = -6 A 52 wl -4*52"* -2* 52 WI 

Converted into degrees 1 - A00 A n ^ ^ 

etc. J * ^ 103 -73 43 

Obliquity of the ecliptic = 23 58' 24" 

-. ABc 

Long, of culminating pt. 

of the ecliptic = yC = 51 30 ; 2" 79 58' 2" 107 24' 49" 

Decli. of cul. pt. = CQ = 18 32' 28" 23 34' 59" 22 47' 20" 
Angle bet. ecliptic and 

meridian = 6 = 74 13' 38" 85 34' 13" Tr-82 21' 1" 

ZNalat. of Zenith = 11 2' 18" 6 23' 52^ 7 8' 40" 

ON = 3 5' 43" 029'40" -057'26" 
7 N = yC + ON 54 35' 45" 80 27' 42" - ' - 106 27' 23" 



BEIHMANA CHRONOLOGY 18i 

ABO 
Parall. in lat. = -11' 28" "6 -6'40"'7 -7' 27" '4 

Lat. of Moon = +23' 17'4 +308'2 + 3651'5 

Corrected lab. of Moon = + 11'48"'8 + 23'27"'5 +29'24"'l 

y=Long. of Sun = 150 13' 9" 150 18' 11" 150 23' 13'' 

yN=Long. of Zenith = 54 35 45 80 27 42 106 27 23 

(yO-yN) = 95 37 24 69 50 29 43 55 50 

Parallax in Long. = + 58' 33" + 55' 65" + 41' 16" 

Long, of Moon <= 148 34 149 46 59 150 59 54 

Corrected long, of Moon - 149 32 33 150 42 54 151 41 10 

Long, of Sun = 150 13 9 150 18 11 150 23 13 

Moon -Sun - -0 40' 36" +0 24' 43" +117'57'' 

Let X represent Moon- Sun, and Y represent the corrected 
latitude of Moon. 

X = -2436" +1483" +4677" 

Istdiff. = +8919 +8194 

2nddiff. - ~ 725 

/. X.= +1483" + 3556'/ i 5t-362''-5< 2 
where t is measured from the instant B and is in units of two hours. 

y = +709" +1408" +1764" 

1st. diff. = +699 +356 

2nd. diff.= -343 

.'. Y = +1408" + 527-"5*-171"'5 I* 
Sum of the semi-diameters of Sun and Moon 

ss 32' 33" '3 = 1953" nearly. 



182 



ANCIENT INDIAN CHBONOLOGt 



Kurukseka 
mean time 


X 


5-8 A.M. 


-2436" 


5-23 


-1907 


5-38 


-1389 


5-53 ,, 


-882 


6-8 


-386 


6-28 


+98 


6-38 


+ 571 


6-53 ,, 


+ 1033 


7-8 


+ 1483 



-410 
I 

-322 
! 

-175 



+ 23 +373 
) 

+ 198 
I 

+303 

'+354 



y 

+ 709* 2587* 

+ 815 2074 

+916 1664 

+ 1011 1342 

+ 1101 1167 

+ 1186 1190 

+ 1265 1388 

+ 1339 1691 

+ 1408 2045 

Time of beginning = 5 h 23 wl +4 w = 5-27 A.M. 
Time of ending _= 6*-53 w +ll m = 7-4 A.M. 

Duration of the eclipse = l^-37 m 

Time of nearest approach of centres = 6* 8 TO +6 OT = 6-14 A.M. 

Minimum distance i= 1154'' 

799 

Magnitude of the eclipse = = 0'41 = 5 Indian units. 

2 x 971 

Time of sunrise in Kuruksetra mean time 

= 5^ 35 W 20* A.M. (without correcting for refraction) 
= 5^ 32 W O 8 A.M. (corrected for refraction) 

.Upper limb of Sun visible at 5-30 A.M. 

The eclipse began almost with sunrise. 



CHAPTER XY 

BE1HMANA CHEONOLOGY 

A Time-Reference from the Jaiminiya Brahmana 

In the present chapter we propose to interpret the following 
astronomical reference from the Jaiminiya Brdhmana : 



J". B'-a^mana, 1, 176, 

This passage may be translated as follows : 

" This was settled by the Brahmanas of former times, 'who 
to-day goes on a journey by passing beyond the opened (mouth) 
of the Dolphin (i.e , the DhanistM cluster)'? The YajMyajniya 
is this Dolphin which stands opening her mouth opposite (the 
sun) in one (i.e., northerly; course. Of that it is verily the food 
oblation by hiding which from her mouth one passes safely/' 

The above translation has been -done by consulting Profs* 
Dr. R. G. Basak, Mm. Sitarama Sastrl and finally Prof. Mm. 
Vidhu&khara Sastri, the Head of the Department of Sanskrit, 

i Cf. the Tandya BraJimana, via, 6, 8-9, which runs thus : 

w& 

IKH 



Caland translates tbia as follows : 

8 A Brabmana, KuSamba ibe son of S.ayu, a Lata^ya (by gotra), used to say 
nboot this chant:'" Who forsooth, will today be swallowed by the dolphin that has 
been thrown on the sacrifice's path?" 

9 Now the dolphin rtrowa on the sacrificed path is the Yajnavajffiya (Mman), 

By saying ' by hymn on hymn ' theriby the ndgat T swallows himself." 

oy eajri g j j moa, vm, 6, 8-9. 



It appears that this reference from the T*t4,a Brffima V a i, practically the same 
ai that of the Jaiminiya Brahmaya quoted above, 



184 ANCIENT INDIAN CHRONOLOGY 

Calcutta University, Post Graduate Teaching in Arts. An 
English version of the German translation of the above passage 
by Caland is given below for comparison : 

" Thus decided the Brahmanas in earlier times : c who is to 
swim away to-day against the gaping jaw of the Dolphin? 1 The 
yajnayaJTilya is the Dolphin who lies in ambush at the narrow 
entrance with jaws opened against the current ; he puts the food 
in the mouth so that he can have a narrow escape as he passes 
by him." 

We are unable to accept Caland 's version. The word 
' prosy ate ' can not mean l swim away/ neither can * ekdyane' 
mean * the current* , nor * apidhaya ' mean by putting.' The 
passage is allegorical which means the time for beginning the 
sacrifice called Yajndyajniya, was settled by the Brahmanas of 
former times by observing the heliacal rising of the Delphinis 
cluster, with which began the sun's northerly course. The food 
oblation was poured into the proper fire when the day began with 
the sunrise and the Delphinis ceased to be visible. The DelpKinis 
t or the Dhanistha cluster always ries north of the east point, while 
the sun at the winter solstice rises south of the same point. 
Hence the Delphinis is spoken of as ' staying opposite the sun/ 

Here the word Sim&uman has been taken to mean the 
Dhanistha or the Delphinis group of stars. The word Sim6u- 
mara literally means a dolphin. The Puranas interpret the word 
8isumara as the star group Little Bear. 1 This meaning has 
been rejected for the following reasons : 

We have seen before that in the Vedas, the ancient Hindus 
had the constellations the two Dogs, 2 viz., the Canis Major and 
the Canis Minor, as also the heavenly boat 3 or the Argonams ; 

1 Visnupu rana , II , 12. 



' At the tail of the iSisumara, are the four stars, named Agni, Mahendra, Kasyapa 
and DJiruva (the pole star) : these four stars of the Stiumara do not set (i.e.. they are 
circumpolar). 

2 ftgveda, X, 14, 10 11, and also -At/iarta Veda, xviii, 2, 1112. Loc. cit. in 
the chapter on Yarna and his Two Dogs. 

S fygveda, X, 63, 20, also Atharva Veda, VII, 63 and XIP, 49. 7, Ibid 



BBiHMANA CHRONOLOGY 193 

= 270 in the year we want to find out. The year arrived at 
becomes 1799 B.C. or 1800 B.C. nearly as before. 

In this chapter we could not use the naksatra divisions as 
used by Aryabhata I, Brahmagupta and as given in the modern 
Surya SiddMnta, which was very nearly true for about 
499 A.D. The history of Hindu astronomy shows that the 
earliest equal division of the ecliptic into 27 naksatras was 
made at the time of the Veddngas and this began with the first 
point of the Dhanistha division fixed by the luni-solar method, 
and we have consequently followed the same method. 

Hence the traditional position of the solstices as stated in 
the Maitrl Upanisat was true for about 1800 B.C., but it would 
be rash to say that this Upanisat was composed at this date. 



85 U08B 



CHAPTER XYII 

BRAEMANA CHRONOLOGY 

Sdmkhdyana Brakmana 

ID this Brahmana in Chapter I, Br. 3, we have the following 
time-reference : 



HT 



" People ask, * in what season should men set up the fires 
again V One opinion is that- it is the rains that are favourable 
for all people for attaining their desires. Hence for the realisation 
of all the desirable things the fires should be set up again at the 
middle of the year ( inan^f ), by observing the heliacal visibility 
of the two stars of the naksatra Punarvasu (viz., a and /3 
Geminorum)." 

"But at this time of observation of the heliacal visibility, 
there may not be the first (light) half of the month. The new- 
moon which comes after the full moon at the Asadhds, happens 
near the two stars of Punarvasu In the rains all the desirables 
are obtained, when the rains set in the Punarvasus are visible ; 
hence in such a new moon the fires are to be set up again." 

The first part of the passage implies that the middle of the 
year, i.e., the summer solstice day was marked by the heliacal 
visibility of the stars a and ]3 Geminorum or Castor and Pollux. 
The concluding portion is a makeshift arrangement, by which 
even the light half of the month is not obtained for setting up 
the fires again. We, therefore, try to ascertain the date when 
the first heliacal visibility of Pollux or ft Geminorum took 



BBIHMANA GHEONOLOGY 195 

on the summer solstice day, the station selected being assumed as 
Euruksetra (30N. latitude). 

Heliacal Rising of Pollux on the Summer Solstice Day 
at Kuruksetra 

In 1941-0, Longitude of Pollux=112 24' 8" 
Latitude =+6 40' 48" 

Let us assume, as a first approximation, the time of the event as 
1100 B.C. The obliquity of the ecliptic at the remote date 
was=28 50' 0" (=) 




PS =66 10' 0". PZ=60 ZS=108 

/. the angle ZPS= 130 1CK 32"; - (D 

E p S= 40 .10' 32" ; . ( 2 ) 

'' V E = 49 49' 23". - 
NowvB=49 49' 28"'. u=23 50' 0" and ^ y EK=iaO, 

- .-. 7 K=6458'2"; "' jjj 

and LE>46 54' 43" ; - (5) 
A ain LB=6 40 1 48" and angle K=46 54' 43" ; 

.-. KL=617'22"; ' "' (6) 

Therefore the arc yL is found from the results (4) and (6) to have 

been =71 15' 24". 

the longitude of Pollux at the reqd. past date 

= 71 15' 24" 
The same in 1941 A.D.=112 24' 8" 

the increase in celestial longitude in the intervening p nod 

=41 8' 44" 
-Hence the date arrived at is about -1022 A.D. 



19.3 ANCIENT INDIAN CHBONOLOGY 

Again in the Samkhayana Brdhmana. XIX. 2, we have 

i a^Rrerrcr , 



''They fahould con serrate them selves on one day after the new- 
moon of Taisa or of Mdgha 9 they say ; both of these views are 
current, but that as to Taisa is the more current as it were. 
They obtain this thirteenth additional month ; the year is as 
great as this thirteenth month ; in it verily the whole year is 
obtained/ 1 (Keith.) 

The Vedic standard month of Mdgha came in our time in the 
year 1935 A.D., between Feb. 3 and March 5. Three years later 
i.e., in 1938, after 37 lunations came the month of Mdgha extend- 
ing from January 31 to March 2. From the mode of intercalating 
a lunar month as found in Vedic literature, viz., one month after 
30 lunations, we readily recognise that the day following the new- 
moon of the month of Taisa or Pousa mentioned in this 
Brdhmana is correctly represented in our times by the date 
Feb. 1, 1938. This day therefore represents in our time what 
was the winter solstice day in the time of the Samkhayana 
Brdhmana. 

Now on Feb. 1, 1938 at Calcutta Mean Noon. 

the sun had the celestial longitude =311 44' 19" 

We deduct from it ...270 0' 0" 

Hence the difference 41 44' 19" 

shows the amount of the shifting of the solstices up to 1938 A.D, 
The date arrived at becomes, 1056 AD., which does not 
differ much from the date, 1022 A.D. arrived at before. 

It is further not very difficult to^find a corroboration of the 
date arrived at, from the rule of setting up the fires again on the 
Asddha new-moon day as stated in reference to) quoted before; such 
a new-moon happened on Aug. 3, 1940 A.D., the conjunction 
took place in the naksatra Pusya, and the moon neared the star 
Pollux in the previous night at about 8 P.M., Calcutta mean time, 
and 

On Aug. 3, the sun's longitude was at Calcutta mean noon 
~13044'17". This was 90 in the time - of the Samkhdyana 



BEAHMANA CHEONOLOGY 197 

Brdhwana showing a shifting of the solstices till 1940 A.D. 
=40 44 ; 17". The date arrived at becomes, 995 A.D. 

Hence the date of the SavikMyana, Brdhmam works out as 
about 1000 B.C. 



CHAPTER XYIH 

BRAHMAN A CHEONOLOGY 
Time Indications in the Baudhdyana Srauta Sutra 

ID the Baudhdyana Srauta Sutra, 1 the rules for beginning 
the year-long sacrifices are stated in the following terms : 



BaudTiayana &rauta Sutra, XVI, 18. 

" They consecrate themselves four days before the full-moon 
day of Mdgha ; thus their purchase of Soma falls on the day of 
the last quarter (Ekastaka). This would be the rule if they 
consecrate themselves without knowing the (beginning of the) 
year. Jf, however, they want to know the (i.e., beginning of the) 
year on the day of the last quarter of Mdgha (Ekastaka, i.e. 
when the first day of the year has already been passed) they 
should consecrate themselves four days before, either the full- 
moon day of Phdlguna or the full-moon day of Caitra ; their 
purchase of Soma would then fall on the 8th day of the dark 
half. By this they do not make the last quarter (Ekastaka) void. 
Their Sutya (i.e. extraction of Soma juice) falls in the first half 
(i.e. light half) of the month, and the (sacrificial) months begin 
in the first (or light) half." 

All this reads like a slightly modified extract from the 
Taittmya Samhitd (vii, 4, 8) or from the Tdndya Brdhmana 
(V, 9), which has been quoted and explained in Chapter 
XIII, 'Solstice Days in Vedic Literature 1 . The author of the 
Baudhdyana Srauta Sutra, here recommends the following of the 

1 Edited by Caland, 1901-1913 A.D. published by the B. A. S. Bengal. 



BB1HMANA CHEONOLOGY 199 

former rules by the performers of the year-long sacrifices. The 
rule of beginning these sacrifices four days before full-moon 
near the Phalgunls, is the oldest that can be traced in the 
Brahmanas. The alternative rule for beginning these year-long 
sacrifices four days before the full-moon day of Magha, was true 
for the time of the Taittirlya Samhita or of the Pdndavas, i.e. 
for about the time when the sun reached the winter solstice 
on the full-moon day of the Vedic standard month of Magha. 
Baudhayana seems to say that on the day of the last quarter 
of Magha, the year-beginning or the winter solstice day 
was already over in his time. Clearly then he does not mean 
the Vedic standard month of Magha when giving his rule. 
His idea perhaps was, that the sun reached the winter solstice 
on the earliest possible day of the full-moon of Mdgha, and that 
the winter-solstice day was inevitably over on the last quarter 
following it. By a full-moon day of Mdgha, he probably means 
a day like the 30th of January, 1934 A.D. Now-a-days the 
winter solstice day is the 22nd of December. This would show 
a precession of the solstice-day by 39 days, and at the rate of 
one day of precession in 74 years, it would indicate a time of 
about 953 B.C. about when, the day of the last quarter of the 
month of Paiisa, and not of Mdgha, could be near to the winter 
solstice day. We shall not be wrong to assume that this Srauta 
Sutra speaks of a time of about 900 B>C. 

This work does not say that the Krttikds (Pleiades) are first of 
the naksatras, as we find enumerated in the Taittinya Samhita. 1 
Nor does it speak simultaneouly of the full-moon days at the 
KrttiMs and the Maghds 2 a statement which is very significant 
as the Pleiades (n Tauri) and the star Regulus (Magha) have a 
difference in longitude of very nearly 90. We miss here state- 
ments like that of the Kapisthala Kaiha Samhita , (a) swmtNf 
tffftgft qqt fefcw 3 (b) <Sn*n$r qwuwirat l^a 4 or of the Maitrdyanl 
Samhita, (c) SRmfaft !OTTOt 6 which mean, 'the Krttikas are 



i Taittinya SamUta, V, 4, 10. 
3 Mahabharata, Vana, 84, 51-52, 
3 and 4 Kap, K. Samhita, VI, 6, 
Satfihit&, IV, 6, 4, 



200 ANCIENT INDIAN CHRONOLOGY 

the head of Prajdpati (year), that sacrifices are to be made on the 
full-moon or new-moon day and that Prajapati is the day of the 
full-moon at the vernal equinox (dgrayam). 9 All these statements 
mean a time about a hundred 3? ears before or after the year 2350 
B.C. - This Srauta Sutra has no statements of the type quoted 
above. 

In another place (XII, 1; Caland's Edn.. Vol. II, page 85), 
Baudhayana lays down the following rule for beginning the 
Rdjasuya sacrifices: 



iit!Hii 5wt^[T^u^ I 

' When a prince is being religiously served with the Rdjasuya 
sacrifice, he consecrates himself by making oblations of clarified 
butter, on the new-moon day which precedes the full-moon day 
either of Phdlguna or of Caitra. 9 

It is difficult to see what season of the year is taken to begin 
on the new-moon which precedes the full-moon either of 
Phdlguna or of Caitra, The former of these new-moons simply 
means the new moon of Magha, which is but a repetition 
6f an older tradition of the winter-solstice day as stated in the 
KausltaU Brdhmana l (XIX, 3). The Mahdbhdrata indicates, 
according to our interpretation, that Yudhisthira was consecrated 
for the Asvamedha sacrifice on the full-moon day of Caitra of 
the year 2446 B.C. The Vedic standard month of Mdgha as 
it came that year was similar to that of "our time in 1932 A.D,, 
and the full-moon day of Caitra of 2446 B.C. corresponded 
with the full-moon day of April 20, 1932 A.D. The new-moon 
day which preceded this full-moon happened on the 6th April, 
1932 A.D. If the Baudhayana rule indicates that spring began 
according to this recorded tradition, the date when this was true, 
would become about 1400 B.C. If Baudhayana, means a year 
like 1927 A.D. on which the new-moon in question happened on 
April 2, the date would come out to have been about 1100 B.C. 
If again it was a new-moon of the type of March 30, 1930 A.D. 
the date of the tradition would be about 886 B.C. In any case 

i JRASBL, Vol. TV, 1938 ; page 42g, 



BBAHMAIS T A CHRONOLOGY 201 

we do not get any clear indication of lime from this reference. 
We shall, however, later on find the day for starting tbe 
Rdjasnya saurifice in the year 836 B.C. A more definite indica- 
tion of the date oi this Srauta Sutra is furnished by the : 
Baudhayana Rule for Naksatresti Sacrifices 

The part of the work where it gives the time for beginning 
the Nctkftttrcsli sacrifices, 1 ruus as follows : 



" Wo now proceed to explain the rule for pert'oiiniug the 
Naksalrexli sacrifice^. Agui wished, M would be tbe partaker of 
food for the yuds/ f riiiM has been set forth by the Bnllimam 
(T. Dr. Hi, L > J, cl . scq. JIH found by Calandj. The full-moon 
which occurs near the Viinkhas has its preceding new-nioon 
once iu the year hi the Bharanl division ; this new-jnoon is 
the day for B<.firtini> fch-j NakMitwsli sacrifice/ 1 

A little lalct* I|MJ rui^s run ap ollows : " 



/' Wefcihali ow\'Xplaiii t!io spocial rnJey : Prajapati the sun 
becoiuos Uplihxn (of wnbdueti light due to the starting of the 
luiifs) on yiatiiiy at the ASlwl division. Heuce all baile/ corns 
become Kanunhliu ibark-y powder mixed with -aird) which are 
to bo mixed with clarified buCter for oblation/* 

Heie ovidiuitly the t ,un is said to reach the vernal equinox 
on thontw.uioon which jince Jed the full-moon in the Viiakha 
divishiii or ii^ar liic ViMtklul 'juncliou 1 stars. Such a new-tnoon 
was oi rare occurrence. Alwu the sun seemed' to turu south at 
the bt^iijiiiug of tin- division A&lvm, an J not*at ila middle. True 
it hsthut this Hrmila tinim ^fiys*"' : 

\ 



rtua ft ra til a tfulra XXYIIf, -4. 
2 ilid., X 
26 110HP. 



202 AXCIEXT INDIAN CHRONOLOGY 

" In the month ot Matjha the sun on getting at the Naksatra 
ilivMon DhnHiti ftj, turns to the north and at the middle of the 
AMcsa division aims to the south in the month of Sravana, These 
are the two limits to the sun's north-south motion." 

This i> evidently borrowed from the Veddngas. This position 
of the solstice? was not true for the time of il e Baudhdyana 
Xrauta Sutra. 

We understand that at the time indicated by Naksatresti 
iuit.- oi" Fmiidhi] iiana, the summer solstice was at the beginning 
of the Ablest! dhision, that the vernal equinox was 
cor>ujut?nth at the end of the first quarter of the Bharanl 
illusion, and the winter solstice was at the middle of the Sravana 
division. 

New the oldest division of the ecliptic began with the ecliptic 
position cf 8-Delphinis as the first point of the Dhanisthd 
division. 

The iuigitude ot ft-JDelphinis in 1935 A JX = 315 26' 5" 
Deduct half naksatra ... ... 6 40 



/. the longitude of the middle of Sravand divn. = 308 46' 5# 
x4gain deduct ... ... - 270 

Hence the long* of the end of the 1st quarter = _ 

of Bharanl division ... ... = 38 46' 5" 

Now the longitude of the sun at Calcutta Mean noon on 
April SO, 1938 A JX, a new-moon day, ms = 39 14' 34//. 

This fairly agrees with the longitude of the last point of the 
1st quarter of the Bharanl division obtained above. 

Here a shifting of the equinoxes till 1931 A.D. of 39 14' 34/7 
indicates a lapse of 1828 years and the date arrived at becomes 
891 B.C. If we want to get at a year near to this date and 
similar to 1938 A.D., that year becomes 886 B.C. or -885 A.D. 

This date appears to be the! time indicated by the Naksatresti 
rule of the Baudhdyana Srauta Sutra. 

THE BAUDHAYANA RULE FOB THE Pancasdradlya Sacrifices 

In another ptoe the Baudhdyana Srauta Sutra lays down the 
following rule for beginning the Pancasdradlya sacrifices. These 
lasted for 5 years and were begun with the advent of the Indian 



BE1HMANA CHBONOLOQY 208 

season of Hemanta or of the dews and ended with the Indian 
season of Sarat or autumn, Hence on the day for the beginning 
of this PailcaSaradlya sacrifices, the desired celestial longitude of 
the sun was about 210. The Baudhdyana rule runs as follows: 



B. S. Sutra., XVIII, 11 

" When a person is being served by tbe five-yearly sacrifice, 
he selects seventeen he-calves which are more than 8 days old 
and of not exceeding one year in age. He makes the sacrifice 
with oblations of clarified butter on the new-moon which precedes 
the full-moon at tbe star group Mrgasiras l (i.e., A, ^, aud 2 , 
Orionis) and secures seventeen she-calves of which the -presiding 
deities are the Maruts or wind gods/* 

The practice was to release 17 he-calces and 17 she-calves 
for freely roaming about in the fields or forests in tbe 1st year, 
17 she-calves in the 2nd year, 17 she-calves in the 3rd year, and 
17 she-calves in the fourth year were also set afc libeity. It is 
not clear if in the fifth year also the same practice was continued. 
The day for beginning the sacrifice was of the new-moon preceding 
the full-moon at the Mrgasiras (i.e., A, 1( Orionis) group. 

Now in the year 1929 A.D., the full-moon near A Qrionis fell 
on December 16 ; and the preceding new-moon happened on 
December 1. We assume here that the sun's longitude increased 
by 60 in two lunations very nearly. Hence the sun reached the 
winter solstice on the day which correspond with the new-moon 
on the 29th January, 1930 A,D. 

On this day, i.e., January, 29, 1930, at 6 M.N. the sun's 

apparent longitude was =308 53/ 1" 

Deduct 270 O'O", 

1 CJ. Apastamba GrJiya Sutra, XIX, 9.3-2, which records a tradition of the 
beginning of Hemanta on the Mrgasiras full-moon day which corresponds to a mean 
date of aboat 2000 B,C, 



203 



ANCIENT INDIAN' CHRONOLOGY 



new-moous answering to the above description happened in the 
year 834 B.C., as the following calculation will show :- 



Ygjir md 


. Julian 


AtG. 


M. Noon 


Remarks. 


date 


days 


Appt. Sun 


Appt. MOOD 




888 A.D. 
April, l'J 


139b651 


19 41' 


104 37' 


J?. M, in Visa'kha Da- 


853 A. D. 
May, 4 


1398666 


34 fi 1' 


23 48' 


N. M. in 5/iaranri3n. for 
setting up fires. 


-SS3A.D. 
June, 3 


13 8690 


62 34' 


58 45' 


N. M. in Punarvasu Dn. 
for setting up fires. 


883 A.D. 
June, 27 


1398710 


75 54 


253 e 0' 


F. M. in U. Asadha Dn. 



Vtidkhd division 
Punarvasu division 
Long, of Pollux 



182 59' to 19619' 
= 62 59' to 76 19' 
= 78 14' 



It is evident that such new-rnoons came in also in tHe year 
895 B.C., i.e. 8 years before the date 887 B.C. arrived at before. 
The Satapatlia Brahmana 1 lays down the rule that fires should be 
set up, on the day of the new-moon with which the lunar 
Vaiakha ended, meaning of course the new-moon, either at the 
Krttikds or the Hyadcs (Rohims). These rules for setting up fires 
by a householder have nothing to do with the beginning of any 
season of the year and do not indicate the date of the Baudhdyana 
Sutra, nor of the 8atapatha Brdhmana, nor of any other work 
of the kind. 

We are thus led to conclude that the mean date for the 
Baudhayana rules for sacrifices should be taken as the year 
887-16 B.C. 



1 Satapatha Brahmana, XI, 1. 1. 7 ; cited by S. B, Dlkfita in his 
, Page 130 (1st Bda.) 



BKAJIiYiAWA HEOKOLOGY 20D 

Again in this year, 880 A.D., 

the longitude of iliG uud of ; he Ibt qr, of Bharayl = 359 3Q/ 

, ,, o 1st pfc. of the V scikha division = 182 59' 

,, >, ,> ,, Mrgntiras ,, = 36 19' 

,. , ,, mid-pomfc of the 8'Civana ,, = 269 39' 

Thus the yenr < Q 87-8fi 15. C. appears to be the mean date indicated 
by the linnclluiynuu rulo- for beghming the Naksatresti, the 
Ptttlcttxtlnuiiijn nnd the Rtljatsuya sacrifices. This date however, 
is linbie to bt-in^ lowered by 7G years or by even a greater 
Juni-soiar period. 

We now ink*; up the Baitdhayana rules for Petting up fires 
by the Loiui'lioltlrr. The rules in quest-ion stale the suitable or 
ausj>icioii,- (fji p >K i'or the purpose and have nothing to do with the 
bogiiu in^s of the ^ensons. The auspicious days are tbe new-moon 
diys jit (1) A>//i7iV7^,(ij tiohhjlft, (H) Punarvaws, (4) P. Phalgttnls, 
(5^ U . PluilyiiHtti and ^ (Hint. A Brahmin is to set up his fires 
in spring, a K's.-itriyu. in .suniuior, a Vaisya in autumn and a 
car-mrtkiT in ihr niirr^. 1 [n this connection it is said: 



\ 

* Th iievv-nionu which follows the full-moon in the Visakhd 
division, onn i happeiiB in a year with the moon in the Rohinl 
division, that is the <iu t v on which the fires are to be set up.' 

This rule* stati 1 * when 1 > get nl the day of a new-moon in the 
lloliini NahtitilrtL f l*heri! is another rule given for settling when 
to fcut tit a nt'w-niuon near the Punaroasus (Castor and Pollux). 



4 Tim lii'W-uioon which precedes the full-moon in the Naksatra 
Jtgtitlln't (here the [7. J,sW/i</;,onc'e (re., on rare occasions) happens 
iu a yrar with tho ujoon nuar the Puna roam (Castor and Pollux) ; 
the tires should l>u set up on this day." 

Tlu'se arc purely luui-solar-slellar phenomena which repeat 
roughly in 8, I J or 19 years. The Rohini and the Punarvasu 

* Bautlba.vami 6. Sutra, 11, 12. 

2 Ibid, III, J, : this iu also repeated in 3CXV, 18. 



205 



ANCIENT INDIAN' CHRONOLOGY 



new-moons answering to the above description happened iu the 
year 884 B.C., as the following calculation will show: 



Tear and 
date 


Julian 
days 


At GL M. Noon 


Remarks. 


Appt. Sun 


Appt. Moon 


-888 A.D 
Apnl, 19 


1398651 


19 41' 


194 27' 


F. M. in Vitakha Dn. 


883 A.D. 

May, 4 


1398666 


34 c 1' 


23 48' 


N. M. in Bh&raniDu. for 
setting up fires. 


888 A.D. 
June, 3 


1398696 


62 34' 


58 45' 
253 c 0' 


N. M. in Piwarvasu Dn. 
for setting up fires. 


688 A.D. 
Jane, 27 


1398710 


75 54' 


F. M. in U. Asa$ha Du. 



ViSdJchd division = 182 59' to 19619' 
Punarvasu division = 62 59' to 76 19' 
Long, of Pollux = 73 14' 

It is evident that such new-moons came in also in the year 
895 B.C., i.e. 8 years before the date 887 B.C. arrived at before. 
The tfatapatha Brahmana 1 lays down the rule that fires should be 
set up, on the day of the new-moon with which the lunar 
Vatfakha ended, meaning of course the new-moon, either at the 
KrttiMs or tbe Hyadcs '(Rohinis). These rules for setting up fires 
by a householder have nothing to do with the beginning of any 
season of the year and do not indicate the date of the BaudMyana 
Sutra, nor of the tfatapatha Brahmana, nor of any other work 
of the kind, 

We are thus led to conclude that the mean date for the 
Baudhayana rules for sacrifices should be taken as the year 
887-16 B.C. 



1 Satapatha Brahmana, XI, 1. 1. 7 ; cited by S. B. Dlksita in his 
130 (1st Eda.) 
R 



BBiHMANA CHKONOLOGY 207 

One point more that we want to notice here is that the 
Baudhdyana Srauia Sutra mentions the name Panini in the 
Pravara section 3 (Vol. Ill, p. 418) and also the name Kaulasva 
Yaska in XVI, 27. Whether these statements place the dales 
of the celebrated grammarian and the author of the Vedic 
lexicon, Nirukta, before the time of the Baudhdyana Srauta 
Sutra (900. B.C. nearly), is a matter that cannot be settled astrono- 
mically, True it is that the word ' Yavandnl ' as found ic Pariini 
means the "written alphabet of the Ionian Greeks, but it would 
be far from rational to conclude that the Yavauas did not come to 
India before the limes of Alexander or cf Darius. 



CHAPTER XIX 

BRAHMAN A CEBONOLOGY 

The Satapatha and the Taittiriya Brahmanas 

The time wben the Satapatlia Bralmana came Juto its present 
indicated by the loiiuwing passage 1 : 

: i 



m 



fc< In this connection they say 'in what season is the beginning 
to be made ?' Some say ' it should be begun in summer, as 
summer is the season for the Ksatriyas and the Avamedha is 
the sacrifice for the Ksatriyas alone. This should be begun in 
spring alone, as spring is the season for the Brahmanas ; whoever 
makes the sacrifice begins it by being a BraMnana 'as *it were. 
Hence this sacrifice is to be begun with the spring alone. 
That beginning takes place on the full-moon night at the 
Phalyus. Six or seven days before it-, come the priests who are 
adhvaryu, hotr, brahmd, udgdtr, etci 

In this passage we get the indication that th6 Indian spring 
at this period, set in at the full-rnoon near the Phalgus or that 
the sun Bad the tropical longitude of 330 on the full-njoon* day 
of Phalguna. In the .earliest Vedic times the full- moon day of- 
Phalguna was the winter solstice* day, and the tyne was about 
4600 B.C. Here we notice a clear statement that the ful moon 
day of Phalguna was the beginning of spring. The -date, "which 
is at the end of this transitional age, has been shown in the next 
chapter as about 65 B.C. Although this Brahmana records 

, * <* * 

i Sattpatha Br&hmwa, 13, 4, 1/2 to 4. Weber^j Edn., page, 979. 



BRAHMANA OHBONOLOGY 209 

the traditions about Yajnavalkya and Janaka of Mithila, 
the present recension of it cannot be much earlier than what has 
been stated above. This change in the meaning of the Phdlguni 
full-moon is also recorded by the Apastamba and Kdtydyana 
Srauta Sutras. 

In the Taittirlya Brdhmana also we have evidence of this 
new meaning of the Phdlguni full-moon day 1 : 



3T sntp^TCTcP I 



i gtsf 5H *3353?t *ns*w i 'ft g^sfamnar^ i 

* * * * 



<1 A Brahtnana should set up his fire in spring. Spring is 
the season for the Brahmaiia ...... what is spring is the first season 

of the year. One who sets up fire in spring, becomes a chief 
among men ......... *.... Summer is the season for the Rajanya 

(Ksatriya). A Vai^ya should set up his fire in autumn and 
aotumn is the season for the Vai^yas. 

" Fire should not be set up on the day of full-moon at the 
P&rva Phdlgunls ( 8 and Leonw). It is the last night of the 
year what is the full-moon at the Purva Phdlguriis ; a man 
becomes a sinner by making fire for the year at the 
fag end. Fire should be set up in the full-moon at the U tiara, 
Phdlgunls ( j8 Leonis and another small star near to it) ; 
it is the first night of the year the full-moon night at the two 
Uttara Phdlgunls. A man becomes wealthy by making fire 
from the very beginning (of the year)/' * * 

Thus in the Taittirlya Brdhtnana also we have a clear indi- 
cation of this new meaning of the Phdlguni full-moon. The date 
for this meaning cannot be much earlier than about 625 B.C. as 
is set forth in the next chapter. 

i Taitiiriya Brahmana, 1, 8, 2, 7-8. 



210 ANCIENT INDIAN CHRONOLOGY 

The question whether the superior limit to the date when 
the lull-moon at the Vttara Phdlgunis marked beginning of 
spring can he raided higher than this 625 B.C., is a very knotty 
one. If it can be established that at the time of these 
Bnlhmanas, the calendar makers could discover the occurrence 
of the second Phalguna as an intercalary month, the date may 
go up to 757 B C. as the following calculations will show : 

On Feb. 27, T 756 AD., at G.M hr. or KM.T., 5-8 
A.M. we have, 

Apparent sun = 330 0' 8". 

Moon = 148 10' nearly, 
and B Leonia = 133 21' 

The full-moon happened 4 hours later, not very far from 
j8 Lconis, the 'junction 5 star of the naksatra, Uttara Phalgunl. 
This full-moon was similar to that which happened on March 
28, 1945 A.1V 

Again as the Satapatha Brahmana has very frequent 
references to Asadha 1 ( vntfi ) 9 which means the full-moon at 
the naksatra, Uttarasadha, we understand that the full-moon at 
this naksatra in Fome years u arked the summer solstice day. 
Now we had on July 1, 762 A.D, a full-moon as : 

On June, 30, 762 A.D , at G.M. Noon. 

Appt. Sun = 89 1' 54", 
Moon - 265 5' 44" nearly 



The full-moon happened about 12 hrs. later, i.e., at about 
5-8 A M. of Kuruksetra mean time of July, 1, and this was also 
summer, folstice day. This full-moon was similar to that which 
happened on July, 31, 1939 A.D. The Satapatha Brahmana 
indicates that the asadhl or the full-moon at the naksatra 
asadha was in some years the summer solstice day and in some 



Cf. Satapatha Brahmana, 2 ch., 6, 3, 12-13 ; 8cb., 5, 4, 1 ; the last reference has 
*W 3lfa whicb Is most a gnificant, Cf . also 11 ch. 4, 2, 5 and c. 



BRAHMANA CHRONOLOGY yll 

years the full-moon at the Vttara Phalgnni marked the cciunp 
ofepring. These two phenomena, of couise cannot happen in 
the same year. 

If the rule-givers or calendar-makers could discover the second 
Caiira as an intercalary month, the date may go up to 'JO I B.<\ 
for the Phalguni full-moon marking the advent of spring We 
had on Feb. 28, 900 A.D., G. M. Noon 

Appt. Sun = 330 24' 56" 
Moon = "l44 59' 50" 
ft Leonis = 131 22' 48". 

This full-moon coiresponds to that on 31st March. 1U34 in 
respect of the.moon's phases near to the fixed stars. 

The corresponding dsddhi fell on the 2nd of July, 906 A JX 
on which at G. M. N., 

Appt. Sun = 89 49' 22" 
Moon = 269 3' 33" 

and Altair orl = 2610 ft, 2g// 
SravancL j 

The full-moon happened in about 14 hrtk It was similar to 
the full-moon on August 1, 1921 A.D. 

It must be said OD the other hand that the Veddnga calendar 
recognises only the second Isadha and the second Pausa as inter- 
calary months. On this basis, the date cannot be raised beyond 
625 B.C. 



CHAPTER XX 

BE1HMANA CHRONOLOGY 

Time References froln the Kdtydyana and the Apastamba 
Srauta Sutras 

In thi> chapter we propose to interpret as far as possible the 
following time references first from the Kdtydyana Srauta Sutra 
and shall ako consider those from .the Apastamba Srauta Sutra. 
Those from the first, work are : 



Pt. I, xiv, 5, 30. 



" The day for being consecrated for the Sdrasvata sacrifice is 
the seventh day of the light half (of Caitra)." 



Pt. II, ii, 1,2, 



" The Turayana sacrifice is to be made on the 5th day 
(tithi ?/ of the light.half of VaisdWia or of Caitra." 



%Jk: cn^rr^N: IIBJI 



Pt. II, xxxi, 4, 34. 

" The second is the five-yearly or the Pancasdracliya sacrifice. 
One who is being served by this sacrifice collects in the light half 
of the month of ZM M , thirty-four animals ( i.e., 17 bull-calves 
and 37 cow-calves) which are sacred to the Maruts to be liberated 
in honour of the Vaisvadevas with the proper sacrificial fees to 
the priests." 



Pt. I, v, l t i. 



-The four monthly sacrifices to be begun' on the full-moon 
day of Phalguna." 



BR1HMAXA CHRONOLOGY 



; u 



1 . 3, 

" The Varunapraghnsa ceremony is to j je p-rur^o.l on ti,* 
full-moon day of Asddha ...... ,., " 



(/") ^ 



l< The sacri6cer who wants a year-long ?aTifrv ^i<v,M 
by performing the SumSirlya sacrifice with Souia or au 
on the day of the first visibility of the crescent beforr *he full- 
moon day of Pkdlgiina ; the sacrifices to continue fiom the 
full-moon day ' - 



(s) " 



Pt. II.sx,!.! . 

The king who wants all his desires to be satisfied *hould 
perform the Asvamedha sacrifice : he should get consecrated for 
it on the eighth or the ninth day or titlii of the Mght half of 
PJialguna." 



\ 

Pt, II, xv, 1, 4. 



" A king should consecrate himself for tl^e Rlja*fiyi sacrifice 
in the light half of Magha." 



(i) 

Pt.II, xiv. 1, 1 

" The Vdjapeya sacrifice is to be done in autumn by people 
other than Vaigyas, i.e., by the Brahrnartas and the Ivsairiyas." 

Of the 9 references quoted above the most striking are the 
references (d) and (e) which tend to show that the full-moon 
day of Phalguna was regarded as the beginning of sprin- and 
that the full-moon of Asddha was taken as the summer solstice 
day or the advent of the rains according to the nature of 
different years of the time. It is evident that both such 
full-moon days as indicative of the starting of spring and of the 
rains, cannot be -comprised in the same year as four lunations 



214 ANCIENT INDIAN CHBONOLO&Y 

= 118 nearly and the two seasons roughly = 122 days. This 
latter period is affected by the position of the sun's apse line. 

Originally in the earlier Vedic period the full -moon day of 
Phdlguna, meant the winter solstice day, when the new- moon 
of Mdgha ended, also meant the same day of the tropical year. 
These phenomena came at intervals of four years as 
4 tropical years = 1461 days nearly and 49'5 lunations = 1460 
days approximately and the moon's perigee playing an important 
part may contribute to the equality of the two periods. 

Now coming down to the time of the Katyayana Srauta Sutra, 
the same day is spoken of or indicated as the beginning of 
spring. We are thus led to a period when the full-moon day 
of Phdlguna came to be interpreted differently. We accordingly 
take tbe full-moon day of PMlguna of the Katyayana Srauta 
Sutra to be a day like the 26th of March, 1937, the latest possible 
day in our time for this lunar phase according to the Vedahga, 
calendar, which was taken for the beginning of apring at the 
time of this Srauta Sutra. 

Now on March 26, 1937 at G. M. N., the sun's apparent 
longitude was =5 V& nearly, and this longitude at the time of 
this tfrauta Sutra was according to our interpretation = 330, 
Hence the shifting of the solstices was 85 26' up to 1937 A.D. 

This indicates a lapse of 2560 years till 1937 A D. and the 
date as, 623 A.D. 

Similarly using the latest possible day for the Isadha full- 
moon day according to the Veddnga calendar in our time waB 
the 29th July, 1931. On this day at G.M.N., the Sun's longitude 
was = 125 23' nearly. As this longitude at the time of this 
Srauta Sutra was = 90 for the summer solstice day r we see that 
the shifting of the solstices till 1931 becomes 35 9 23' nearly, 
indicating a lapse of 2560 years and the date as, 629 A.D. 

Thirdly by considering the reference (6) as to the Turdyana 
sacrifice day, we take the <lay in question as similar to April 
25, 1936 A.D. which was the vernal equinox day of a year at the 
time of the Srauta Sutra. 

Now on April 25, 1936 A.D. the sun's apparent longitude 
was~35 l', which represents shifting of the solstices, and the 
year arrived at becomes, 624 A.D. 



BEIHMANA CHRONOLOGY 



Fourthly it is possible to arrive at the date, 624 A.D fiom 
reference (c) from the Pancasaradlya sacrifices. The 5a\ li 
question appears to have been the Anumati fuli-moun day of 
Afaina. 

-The reference (/) is an echo from the Satapatha Br'linthnw, 
ancf this Srauta Sutra is a crude follower of an old rule. The nM 
of the references do not present any peculiarly interesting 
feature. 

A calendar for, 624 to 623 A.D. and for one dav oi, 1>29 
A.D, are shown below, giving the saorificially important itou** : 

Luni-eolar Elements at G. M. N. 



Julian 
Calendar 


Julian Days 


Appt. Sun 


Appt. Moon 


Remark? 


-629 A.D. 
Jan. 30 


1491416 


8950'8" 


26932' 


Summer Solstice day on 
Isadlia IT. M. day. Varuna 
PragMsa to start 


-624 A.D. 
Mar. 27 


1493228 


35948'3" 


54*4' 


Lunar Vaisaklia, 5th day of 
light half. V. Eqirinux hy, 
Turayana sacr : fice dav. 


-624 A.D. 
April, 6 


1493238 


9*271 8" 


18158' 


F. M. near a Libra TisdMfi) 


-624 A.D. 
Sept. 29 

, . 
-623 A.D. 
* Feb. 25 


1493414 

, ' 
1403563 


179*40'23" 
; . 
33017'1" 


353"23' 


Anumati F. M. diy on Au- 
tumnal Equinox day. Panca- 
taradiya to start. 


14434' 


F. M., in 17. Phalgum spring 
begins Caturmasya^to st*- 



of Equinoxes from -624 to 499 A.D. = 1532'28". 
The D^nistM naltsatra extends from 27747'32" to 2917'3" 

34427'32 ff to 35747 ; 32 /; 
AMni , > " 

Uttara Phalgunl 
Uttara Asadha 
ViiakM 



to 

26427 / 32 /y 
18427'32' / to 19747'82" 



We . thu. M to concede ,hs 



other evidences, 



218 ANCIENT TNTHAN CHRONOLOGY 

We give the translation by Mrs, "Rhys Davids 1 : 
" The Exalted One was once staying at Savatthi. Now at 
that time Chandima, son of the Devas, was seized by Rahu, lord 
of Asuras. Then Chandima, calling the Exalted One to mind, 
invoked him by this verse : 

O Buddha MIero ! glory be to thee ! 
Thou art wholly set at liberty ! 
Lo ! I am fallen into dire distress ! 
Be thon my refuge and nay hiding place ! 
Thea the Exalted one addressed a verse to Rahu, lord of the 
Asuras, on behalf of Chandima, son of the Devas : - 
To the Tathagata, the Arahant 
Hath Chandima for help and refuse gone. 
O Rahu, set the moon at liberty ! 
The Buddhas take compassion on the world." 
We nest cite the section or sutta : 

10. Suriyo. 

1. Tena kho pana Sanaayena Suriyo devaputto Rahuna 
asurindena gahito hotill Atha Kho Suriyo devaputto Bhagavantatn 
anussararaano tayain velayam imam gatham abhasi il II 

2. Namo te Buddha Vjra-tthu !! Vippatnuttod sabbadhi il 
Sambadhapatippanno-sini II ta^sa m^ saranam bhavati II II 

3. Atha Kho Bhagava Suriyara devaputtarh arabha 
Rahum asurindara gathaya ajjhabhasi II II 
Tathagatam arahantam II Suriyo saranani gato II 
Rahu pamunca Surly am II buddha lokanukampakati II II 

To andhakare tamasi pabhamkaro II 

Verocano mandali uggateio II 

Ma Rahu gilicaram antalikkhe || 

Pajam mama Rahu pamunca Suriyan-ti II II 
Mrs. Rhys Davids' translation runs as follows : 
" Now at that time, Suriya, son of Devas, was seized by Rahu, 
lord of Asuras. Suriya, calling the Exalted One to mind, invoked 
him by this verse: 

Buddha ! Hero ! Glory be to thee ! 

Thou art wholly set at liberty ! 

1 The Bpok of the Kindred Sayings (Samyntta-Nikayd). pages 71-73 



INDIAN ERAS 21ft 

Lo! I am fallen into sore distress. 
Be thou my refuge and my hidiny-place ! 
Then the Exalted One addressed a verse to Rfiliu . lord of 
Asuras, on behalf of Suriya, son of the Devas : 

To the Tathagata, the Arahant, 
Hath Suriya for help and refuge gone. 
O Kahu, set the sun at liberty I 
The Bnddhas take compassion on the world. 
Nay, BShu, thou that walkest in the sky, 
Him that thou chokest, darkening the world. 
Swallow him not, the craftsman of the light, 
The shining being of the disc, the fiery heat, 
My kith and kin Eahu, set free the Mm '." 

We understand that the eclipse of the moon was closely 
followed by an eclipse of the sun, and apparently at a very short 
interval, viz., of a fortnight, as the phrase ten* Ifho pan* summjen.i 
(If* g 3* *mfcr) indicates, i.e., the two events happened 
in the short period of time of the Buddha's stay at Sravasil. 

Now the mere happening of two eclipses, one of the moon 
followed only a fortnight later by on. of the sun, is not quite 
adequate for settling our problem. We. want one more 
circumstance of the eclipses, .,*., the lunar month in wh.ch 
these two eclipses were visible at Sravast, The D ,,. 
contains ten suttas in all, of which two , ,ate 
one each to Jftgfcc,, Mifgudha. D.nnam Kanu^ 
and Surio. All or these a,e 



eng to the Hindu 
number. 1 They are the eight 7am, eleven Rudras, twehe 

^'S^M- -y be .dentined ,Uh 
tbe^sidL deity of the five-yearly 
The twelve mtyas are the twelve 



220 ANCIENT INDIAN GHBONOLOGY 

is spoken of here as Magha Devaputta in the Saniyukta Nikaya. 
In the Devapntta snlta it is said that first came Kassapa> to meet 
the Buddha, then came Magha and tbeu came the rest. So far 
as we cm understand 'of the allegory underlying these suttas, the 
winter solstice day marking the advent of Kassapa or Prajapati 
came first, then came the full-moon ending month of Magha t 
a Devaputta with the fall-mxm near the naksatra Pusya. The 
Devaputtas of the section are probably some other gods either of 
the Hindu or of the Buddhist tradition. 

The two consecutive eclipses spoken of in the Saniyukta 
Nikaya most probably happened, in the following order : 

(1) Kassapa or the winter solstice day came first. 

(3) An eclipse of moon followed it at about the ' junction 
star ' S-Cancraj. 1 

(8) An eclipse of the sun came a fortnight later. 

Thus the solar eclipse happened in the middle of the full- 
moon ending Magha aud the lunar eclipse at its beginning ; 
both the astronomical events were observable from SravaslI 
where the Buddha was staying at the time. 

Now on looking up the work Canon der Finsternisse* we 
find that in the period of time from 580 A.D. to 483 A.D., the 
only eclipses first of the moon and then of the sun at as interval 
of a fortnight, of which the solar eclipse happened at the middle 
of the full-moon ending Mayha, and both the eclipses were 
visible from Sravasti, were : 

(1) A lunar eclipse on 

December 29, 559 A.D. (560 B.C.). Julian day no. = 1517246. 
Full moon happened at 17 hrs. 30 in. G-.M.T. or 23 hrs. m. 
LS.T. Magnitude of the eclipse = 6*8 Indian units. 
Duration of the eclipse = 2 hrs. 40 mius. 



1 At this period of vime a full moon at about 3* behind S-cancra gave the 
winter solstice day. For on December 27, 576 B C. at G M. Noon App. Sun = 
270 17', App. Moon = 95 57' and $-canGr& = 93 nearly, Full moon happened 
about 5-12 A.M. I.S.T. and $un reached the winter solstice at about 10-45 A.M. 
I.S,T. 

3 The freat book on eclipses by Oppolzer, Vienna, 1887* 



EEAS ^21 

(2) A. solar eclipse on 

January 14, -558 A.D (559 B Cj, Julian day no. = 151720d, 
New moon happened at 6hr?. 38 in. G.M.T. or l'2hiv, .Mr. l.ij.T. 
Longitude of conjunction of Sun and Moon = 28S G *40l. 

The central line of the annular eclipse pa^ed ihrouuh the 
three places A, B and C having the following ion^mi^ ami 
latitudes : 

Station Long.' Lat. Lncatiwi of Station 

A 80 E 85 N 150 miles west of Cyprus 

B 80 E 31 C N Nanda Devi Peak of the Hininiayns 

119 E 57 N A place in East Siberia. 

Both these eclipses were visible from Sravasti in the di.-triu 
of Rae Barelli; the first was a partial eclipse of the moon ami the 
second though an annular eclipse was a partial one at Sravasti. 
The &un had reached the winter solstice 18 dajs before the day of 
the solar eclipse, i.e., on the 27th December, 560 B.C. 

If we accept that the Buddha's Nirvana happened in 544 
B.C. or -543 A.D., the eclipses in question as referred to in the 
Samyutta Nikaya, happened 15 years before that date. The other 
finding of the Nirvana year as 483 B.C. becomes 76 years later 
than the year of the eclipses. If the tradition of the eclipses is 
true and our interpretation of the month of their happening be 
correct, the year 483 B.C. for the Buddha's Nirvana is inadmis- 
sible. Here the Ceylon-Burma tradition as to the N/rra>t-year, 
viz., 544 B.C., is really the true date of the great event. 



CHftPTER XXII 

INDIAN EEAS 
Kaniska's Era 

The eras used in the Kharosthl inscriptions are still a matter 
for controversy. Di\ Sten Konow in his celebrated edition of 
them in the Corpus Inscriptionum Indicarwn, Vol. II, pp. 
Jxxxii-ixxxiii, has collected together 36 instances of dates from 
these inscriptions and hai divided them into two groups, A and B. 
The dates used in Group A belong to an earlier era, while 
those iu Gronp B use the era or the regnal years of Kaniska. In 
this chaptei we propose to ascertain the era used in this second 
Group B Of the dates in this latter group only those which are 
found in Nos. 26 and 35 ^ive us some clue as to the era used, 
t?f., 26 Zeda. saw 11 Asddhasa masasa di 20 Utaraphagune is'a 
Ksunami marodasa marjhakasa Kaniskhasa, rajemi. 

35 Und. Saiii 61 cctrasa mahasa divasa athami di 8 ise 
Ksunami Purvdsadlie. 

These instances state that in the eleventh year of king 
Kaniska on the 20ih day of lunar ( Asadha, the moon was con- 
joined with the iiaksutnt Uttaraphalguni, and that in the year 
61, of Kaniska, the moon's nalcsatra was PurvsatldhTi, on the 
8fch day of caitra. Prom some examples of date in the Kharosthl 
inscriptions Dr. Konow has come to the conclusion that " the 
fall-moon day must be the first day of the month," the chief 
example being that the first day of Vai^akha was taken as the 
full-moon day of Vaistikha (samvatsare tiSatime 103 vesakliasa 
dwase prathamime di atra punapakse No* 10, Group A of 
Konow's list). Here there is no room for a difference of opinion 
with Dr. Konow. But T have to say that this system of reckon- 
ing the fnll-moon ending lunar months is not Indian, it may be 
Greek or it may be Babylonian. The month that is called 
Vaiakha in this inscription would be called the full-moon endin* 



INDIAN ERAS 223 

lunar Jyaistha according to the Indian rerkonii;,.. l\ tv* 
Mnha'bharuta also we have "the full-moon near the ."/:;, i- 
about to come and the month of Mtiglia is al>o draw in, MM> 
close." 1 

Now accepting the reckoning of the full-moon endinu moitK* 
as reckoned in the inscriptions, the meaning it clear ihat :lu* day 
that is spoken of as the 20th of Asadha, is the 5th da v ot 
new-moo-i ending Sravana and the 8th day of Caitm i-* <le >th 
day of the dark half of Caitra. Hence we have the diitp* as: 
(0 Year 11, month .Snivana, 5th day, Uttaraphahinni. 
iii) Year 61, month Caitra, 23rd day, Purmlstidlw 
Dr, Fleet is of opinion that the well-known Saka pra iiiJ ilie 
Kaniskaera are but one and the same era. Now the year* 11 
and 61 of the Saka era are similar to the years IJhio and 1937 
A.D. of our times in respect to luni-solar stellar aspects and 

(a) In 1925 A. D., on July 26, the moon's mksatra wa- U. 
Phalgiml, and it was the day of 5th titlri of li^ht half of 

Smvana. 

fb) In 1937 A.D., on April 4, the moon's nateatn was 

P. Asddhd. 

But the iih April, 1937 A.D. is shown in modem Hindu 
calendars as the 8th day of the dark half of Phalgm<< It may 
be observed, however, that the Vedic standard month of tog**, 
came in the year 1935 from Feb. 3 to March 5, and that no 
intercalary month would be reckoned in those da } , of pie- 



I Mm., AtvameMa, Oh. 85. 8 :- 



224 ANCIENT INDIAN CHRONOLOGY 



Brahmagupta says " 
Kali year** were :>179 (elapsed) at- the death of the Saka king/* 
Again Brahmagupta calls the years of the Saka era as " the years 
of the Saka kings (^rayrrtT^ HI wijt^w 1 * ^Ta ' WlfotciW*," 2 i.e., 



when 550 years of the Saka kings had elapsed). Hence the 
regnal years of king Kaniska may not be the same as the years 
of the Saka era as used by the Hindu astronomers. It seems 
likely that the Saka era was started with the death of the prede- 
cessor of Kaniska whose real accession to the throne came in the 
year 78 A. D., while his regnal years -were reckoned from the 
year of his coronation. On this hypothesis Kaniska's regnal. 
years or his era were started at a very short interval from 
78A.D. 

In the Paitdmaha Sidclhanta as summarised by Varahamihira 
in his Pajicasiddhantikd , the epoch used is the year 2 of the 
Saka kings 3 : 



" Deduct 2 from the year of the Saka kings, divide the result 
by 5, of the remaining years, find the ahargaya from the beginning 
of the light half of Mdgha starting from tHe sunrise of that 
day." 

We can, now readily show that we may take the regnal 
years of Kaniska to have been started from this year 2 of the 
Saka kings. 
On this hypothesis, we have, 

the year 2 of Saka kings=80 A.D. 
.'. the year 11 of Kaniska =91 A.D. 

The year 91 A.D. is similar to the 1927 A.D. of our time 
for the No. of years lapsed = 1836, and 1836 = 160 x 11 + 19 x 4 . 
Hence the 20th day of Isadha of the inscription is similar to 
Tuesday, the 2nd August, 1927 A.D. 

Again the year 61 of Kaniska=141 A.D. and the year in our 
time similar to 141 A.D. is readily seen to be 1939 A.D,, and 

1 B. Splnitasiddhanta, i, 26. 

2 Ibid, XXIY, 7. 

3 PpficasiddMntilia, xii, 2. 



INDIAN ERAS 225 

that the date of the inscription corresponds to Tuesday, the llth 
April, 1939 A.D. 

Now the interval between 1939 A.D. and 1927 A.D. = 12 
years, whereas between the year 31 and the year 61 of 
Kaniska the interval is 50 years. Now as 50=19x2 + 12, the 
moon's phases near to the fixed stars which repeat in 50 years 
also do' repeat in 12 years. It is therefore quite consistent to 
take king Kaniska's regnal years to have been reckoned from the 
year 2 of the Sak* king?, 

It now remains (fl to determine how and when the year of 
the Saka kings was taken to begin initially, (ii) why the lunar 
months were reckoned from the full-moon day itself, and (fit) to 
verify, by back calculation, the dates mentioned of the years 11 
and 61 of Kaniska, 

With regard to the first point, we know that in Vedic times 
the year was taken to begin from the winter solstice day or 
from the day following; in the Vedanga period also, the year 
was begun from the winter solstice day. As the time when the 
Saka era came to be reckoned, was before that of iryabhata I 
(499 A.D.),. we may reasonably assume that originally the Saka 
year also was begun from the winter solstice day. 

We assume further that the winter solstice day was correctly 
determined 5 years before the Saka year 2 or 80 A.D. The 
number of tropical years between 75 A.D. and 1900 A.D. = 1825, 
which comprise 666576 days nearly. On applying these days 
backward to Dec. 22, 1899 A.D., we arrive at the date Dec. 24, 
74 A. D., on which at 

G. M. Noon Hence on Dec. 22, 74 A.D., at G.M.N., 



Mean Sun = 270 56' 21"'ll 
Moon = 121 15' 31"'75 
Lunar Perigee = 231 39' 49" '94 
Sun's Apogee = 69 58' 35"*32 
,, Eccentricity '01747191. 



Mean Sun 268 58' 4"'45 
Mean Moon = 94 54' 21"'69 
L. Perigee = 231 26' 27" '83 
Appt. Sun = 269 38' 
Appfc. Moon = 91 44' nearly. 



Thus on Dec* -22, 74 A.D. the full-moon happened about 
4 hours before G s M. N., and the sun reached the winter solstice 
in about 7 hours. 

89 1408B 



226 ANCIENT INDIAN CHRONOLOGY 

This elucidates the points ff) jnd A'O, t"., that the Sdka year 
was initially taken to begin froni the winter solstice day, and why 
t?e months were reckoned from the full-moon day itself. In 
75 AJX, the mean longitude of Pollux was 8631', nearly : the 
moon at opposition on Dec. 22, 74 A.D., had the longitude of 
about 8928', i.e., about 3 ahead of the star Pollux, and the day 
was that of the fnll-moon of Pausa, and similar in our times to 
that which happened on Jan. 15, 1930. 

The actual start-ing of the era of Kaniska may have taken 
place, on our hypothesis, from the full-moon day of Dec. 26 of 79 
A .IX as the first day of lunar Pausa. This agrees with the 
statement of the inscription that the Vaifakha masa had the first 
day on the day of the full-moon near the VisaWins. ."We shall 
also show later on that the Saifwat months were also full moon 
ending. 

Having thus shown why the era of Kaniska may be taken to 
have been started from the 26th December, 79 A.D., we now turn 
to determine the date for Sam 11, Asddha mdsa, di 20, Uttaraphal- 
guni. Evidently the date was similar to Aug. 2, 1927 A.D., and 
between these years tie interval was 1836 years, which comprise 
670611 days nearly. We apply these days backward to Aug. 2, 
1927 A.D. and arrive at the date, July 8, 91 A D., and on July 
7, 91 A.D. at G. M. N., 



Mean Sun = 104 14' 60* '20 
. Moon = 146 41' 8* '90 
Lunar Perigee = 184 37' 5"*67 
Sun's Apogee =*70 15' 34"*87 
Eccentricity = '017466. 



Hence- 

Appt. Sun = 103 7' 

,, Moon = 142 36' 
and the "junction star" 
U. Phalgunl = 144 46'. 



Again 19 days before this date,i'.e., on June 19, 91 A.D., 

at a. M. N.-- 



Mean Sun = 85^ 31' 11"'93 

Moon = 256 12' 54*53 
Luaar Perigee = 182 30' 5"'64 



Hence 

Apparent Sun = 85 0' 
Moon' = 261 



INDIAN EEAS li7 

thus the full-moon happened about 8 hours later, and this 
was the first day of the month. Hence tha 8th of July, 91 \ D 
was the 20th day of Asadha, and it has been made clear that' 'the 
moon on this day got conjoined with /3 Lconis or Uttarttpkalguai 
in the evening. The date of the inscription was thus Jnlti 8 
91A.D. * ' 

Next as to the year 61 of Kaniska = Saka year 63=141 A.D , 
the moon on the 8th day of the dark half of (Jaitra, was conjoined 
with the naksatra PurvasddM. The day in question was similar 
to. April 11, 1939 A.D. of our time. The number of years 
between 141 A.D. and 1939 A.D. was 1798, and in 1798 sidereal 
years there are 656731 days. These days applied backward to 
April 11, 1939 A.D., lead us to the date-- 
March 17, 141 A.D., on which at G. M. N., 
Mean Sun = 353 44' 43"'00 



Moon = 258 15' 1'12 
Lunar Perigee = 46 46' 56"' 27 
Sun's Apogee = 71 6' 27" 69 
Eccentricity = '017447. 



Hence 
Appt. Sun = 355 41' 
Moon = 1254 14', and 
P. Aqadha = 248 43' 
(8 Sagittarii) 



w 

Here the conjunction of the moon with 8 sagittarii on thia 
day was estimated in the previous night. The day in question 
was of the 7th tithi according to the siddhantas, and the day of 
the last quarter was the day following ; bat this day was the 8th 
day of the month. 

For on the 10th March, 141 A.D., at G. M, N., 

Mean Sun = 846 50' 44* '70 



Moon = 166 0' 55" '92 



Hence the full-moon 
had happened about 



3 hrs. earlier. 
Lunar Perigee = 46 V 9" '50. 

This was the full-moon day and the 1st day of Caitra ; hence 
the 17th March was the 8th day of the month. 

Thus we see that the hypothesis that the era of King Kaniska 
was started from Dec. 25 of 79 A.D. or from the year 2 of the 
gdka era, satisfies all the conditions that arise from the dates given 
in the Kharosthi inscriptions, Group B, of Dr. Konow. The 



228 ANCIENT INDIAN CHRONOLOGY 

present investigation shows that the Sdka emperor Kaniska lived 
at the beginning of the Saka era, a view which, I hope, would be 
endorsed by all right-micded historians and it would not go 
against Dr, Fleet. When this solution of the problem is possible, 
we need not try to find others leading to other dates for the . 
beginning of Kaniska's regnal years. 

Dr. Van Wijk, the astonomical assistant to Dr. Konow, has 
tried to show that the era of Kaniska was started from 128 A.D., 
and would identify the regnal year 11 of Kaniska with 139 A.D. 
He based his calculation on the modern Surya siddhdnta, which 
cannot be dated earlier than 499 A.D. Without examining his 
calculations we can say that his findings are vitiated by the 
following grounds : 

(a) The Gaitra suklddi reckoning of the year as found in the 
modern Surya siddlianta, cannot be applicable to the early years 
of Ska era and Kaniska's regnal years which were prior to 499 
A.D. 

(6) The word " day of the month " means simply a day and 
is not to be confounded with a tithi as used in the modern Surya 
siddhanta. 

(c) The word " naksatra" mentioned in these inscriptions 
meant very probably " star clusters " and n&t ^Vth part of the 
ecliptic* 

For these reasons I have used the most accurate or up-to-date 
equations for finding the sun ard the moon's mean elements 
instead of following the Surya siddhdnta. The luni-solar periods 
used in this investigation are also most accurate and deduced from 
the constants as given by Newcornb and Brown. It has been 
shown that the days of the month are also " days " and not tithis 
and naksatras mean <c star clusters " and not equal divisions of the 
ecliptic, I have taken the data from the inscriptions as actually 
observed astronomical events. 

It seems that Dr, Van Wijk has done disservice to himself, to 
Dr. Konow and to history by lowering the era of Kaniska, as to 
its beginning, to a very improbable d$te of about 128 A.D. In 
our opinion he should have made a thorough study of the history 
of Indian astronomy before making any chronological calculations 
for any date prior to 499 A.D. 



CHAPTER XXIII 

INDIAN ERAS 
Earlier Era of the Kharosthl Inscriijtioi,fs 

We have in the preceding chapter shown that Kaniska succeed- 
ed to the throne most probably in the year 78 A.D., and that his 
regnal years or his own era was slatted froin 80 A. D. In the 
present chapter we shall try to ascertain the era or era*, used iu 
Dr. Konow's list (A) in his Inseriptionum Indicarum, Vbl I, 
page Ixxxii, of the instances of dates of the earlier Kharosthi 
inscriptions. This list contains 23 dates of the inscriptions ; the 
23rd states the year as 

23. Skara Dheri : Vasa ekunacadu&utime (399), AsadJi^t 
masasa divase 22. 

In the Taxila copper plate of the year 78, the Greek month 
Panemos is used and stated as "Panemasa masa". These 23 
inscriptions record years serially from 58 to 399. It is for the 
archeologists to pronounce whether it would be rational to take 
all these instances as belonging to the same era. One outstand- 
ing fact is the statement in No. 23, that the year is mentioned 
as 399. Further the months are taken to begin on the full-moon 
day the Vaiiakha ntSta had its first day on the day of the full- 
moon near the Ftffifchfla. Such a month in the strictly Indian 
calendar would be called Jyaistha (and not ftitttto) full-moon 
endino- Hence the month of Pausa of these inscripfcons began 
on the full-moon day of Pan* and ended on the day before the 
full-moon of Mdgha. The year of these inscriptions began as m 
the case of the Malava, and Saka eras with the full-moon of 
Pausa- the types of Pausa of these were, of course, different 

Tow deducting 80 from 399, we arrive at the year a 
320 B C Again the shifting of the equinoxes and the s 
tH 1940 AD becomes about 31" 24' nearly. Hence what was 
tnelltdeonhesunof 270= iu the year 320 B.C. would in 



230 



ANCIENT INDIAN CHEONOLOGY 



year about 194.0 A.D ., become 301 24' nearly, a longitude which 
the sun has on the 22nd of January nowadays. 

On looking up some of the recent calendars we find that there 
was a full-moon on January 23, 1932. Now the number of 
years from 320 B.C. to 1940 A.D. = 2259 years and 2259 = 1939 x 
1 + 160x2. Hence 2259 sidereal years represent a complete 
luni-solar cycle comprising 825114 days. We apply these days 
backward to January 23, 1932 A.D. and arrive at the date 

December 26, 329 B.C., on which at G. M. T. hr., 



Mean Sun = 26952'7"*16, 

Mean Moon =9059'59"'31, 

Lunar Perigee = 7248'8"'65, 
Sun's Apogee -687'11" 
Sun's Eccenticity=-0176l3 
2e=121'.G98, |e 2 =l / '334 



Hence 

Appt, Sun = 27048' 
Appt, Moon=9236 nearly. 
F. M. had happened about 3^ 
hrs. before and the sun reached 
the winter solstice 19 hrs. before. 



Thus Dec. 25, 329 B.C., was a full-moon day according to the 
Indian mode of reckoning of those days, and it was the day of the 
winter solstice as well. Hence the year could be begun astronomi- 
cally from this date which was both a full-moon day and the 
day of winter solstice. This means virtually starting the era from 
the year 328 B.C., Jan. 1. This year almost synchronised with 
the year of the Indian expedition of Alexander the Great. If, 
however, it is considered that the year was started, not from 
the winter solstice day but from the day, following we find that 

On Dec. 26, 310 B.C., at G.M.NL, 



Mean. Sun 
Mean Moon 
Lunar Perigee 
, Sun's Apogee 



=26945'56"'90, 
=8835'38"'90 
= 12556'19*'-55 
= 63 26'47* 



SuB 7 s Eccentricity =017613 



Hence 

Appt. Sun =27041' 
Appt. Moon85l5' nearly. 



We readily see that the full-inoou came in about 9 brs, more, 
and this date was the day following the winter solstice. If the 
era, of which we want to find the beginning, was really started 
from such a correct determination of the winter solstice day on 
this 26th of Dec. 310 B.C. The 1st day of lunar months would 



INDIAN EEAS gg, 

be a full-moon day. On the whole this date was mo^t f.,vo,rahl, 
for the starting of the era O f the earlier Khmotilii in^np,;,,^ 
The usual practice, however, of beginning an era wa, i,, i-,ei,;un 
it from 5 years later. Hence the actual reckoning of the era wa- 
probably made from the full-moon day of about TV, -'0 
305 B.C. ' " ' 

Now we know that Seleucus's c-ra was contemptou-.! from 
about 312 B.C., and was actually started from the jear 305 B.C. 
It would thus appear that the era which the earlier K/i.iW/,/ 
inscriptions use may in all probability have been this, era. 

Hence 

The Kharosthi Inscription year 

f 

58 represents 247 B?C. 

78 227 B.C. 

103 202 B.C. 

136 169 B.C. 

187 118 B.C. 

384 M 80 A.D. 

399 95 A.D. 

The archaeologists alone may say if this determination 
represents the nearest approach to reality. If we accept the 
hypothesis that the era used in these inscriptions is really the era 
of Seleucns Nikator, who in all probability is referred to as the 
Maharajatiraja, there would be a slight overlapping of it with the 
era of Kaniska started from 80 A.D., which is permissible. If the 
Kharosthi inscriptions her use the era of Alexander the Great, 
this was probably started from about 827 A.D., there would be 
no overlapping with Kaniska's era. My own independent 
view is that Seleucus's era meets all the conditions of the era used 
in these inscriptions and the slight overlapping with Kaniska's 
era is permissible, as has tfeen said before. If Dr. Konow ha* not 
really been able to get at a true chronological order in making up 
his List A, some of the inscriptions might belong to other eras of 

later beginning. 

Next we have to consider the interpretation of Dr. Luders, 
who has opined that the era of Maharajatiraja 292 or 299 was 



232 ANCIENT INDIAN OHBONOLOGY 

really the Parthian era btarted from 248-247 B.C. 1 We have to 
differ from him. Kaniska's era could not have been started 
from 328 A.D. as has been shown in the preceding chapter. Dr. 
Van Wijk is wrong in his calculation. There was no one king 
in these dajs who was styled Maharajarajatiraja. Kaniska was 
one and another was a Kusana (Taxila silver scroll of the year 
136). The title in its Greek form was very probably first 
assumed by Seleucus Nikator. The same title may have been 
assumed by or ascribed to the great Maurya Emperor A&>ka. Our 
results of calculation are set forth below : 
On Dec. 26, 272 B.C., at G. M. T. hr., 



Mean Sun=270 3' 10"'72, 

Moon =90 21' 38" '07, 

Lunar Perigee = 64 &. 



Hence 

Appb. * Sun=27057', 
Moon=8725 / , nearly. 



Sun 's Eccentricity = '017613. 

It was the day following the winter solstice day, and the full- 
moon (of Pausa) came in about 7 hrs. more. Thus this date was 
quite suitable for the starting of a new era. The date shows a 
peculiar coincidence with that of Afoka's accession to the Maurya 
Empire. The real starting of Asoka's regnal years may have 
been started five years later, from about Dec. 29, 267 B.C. It is 
again not unlikely that an era may have been started by 
Ghandragupta Maurya, the grandfather of Asoka, from about, 321 
A.D. We are here dealing with probabilities, but we must not 
forget that the last year recorded in the Eharosthi inscription of 
Skara Dehri was the year 399, and there should not be much 
overlapping between the regnal years qf Kaniska, and this older 
era of the Kharosthi, inscriptions. Of Kaniska the first regnal 
year can not much move from 78 A.D., the zero year of the Saka 
kings. The luni-solar phenomenon which led Dr. Van Wijk to 
identify the regnal year 11 of Kaniska with 139 A.D., was true 
also for the year 90 A.D. This would "make the regnal years of 
Kaniska possible for being started from ?9 A.D. It is well 
known that such luni-solar pheLomeoa repeat in cycles of both 19 
and 11 years. The 49 years which intervene between 139 A J). 

1 Ct Icarya-puwafijali, published by the Indian Research Institute, Calcutta, 
1940, page 288- 



INDIAN ERAS 233 

and 90 A.D., comprise two cycles of 19 years and one cycle of 
11 years. There can thus never be any possibility for an absolute 
fixing of the date of any past event by such luni-s^iar phenomena 
or events. We have also to respect tKe tradition and also to depend 
on the position of the equinoxes or of the solstices if either is 
discernible or can be settled. Dr. Konow and his astronomical 
assistant Dr. Van VISijk" Kave shown a total disregard for 
tradition and tKe latter has depended on a very slender evidence 
like a simple luni-solar event. This can not but be called irrational 
and no chronologiat would lend his support to such a finding. 

As to Dr. Van Wijk's identifying th'e regnal years 11 ani 61 
of Kaniska with 139 A.D. and 189 A.D., we can readily examine 
the validity thereof in tKe following way : 

The luni-solar cycles according to tK& Suryasiddhanla are 
3, 8, 19, 192, 263, 385 and 648 years. Hence the Christian years 
in present times whicK were similar fo 139 A,D'. and 189 A.D. 
are respectively 1923 A.D. and 1935 A.D. The day which' 
corresponds to Awdha rnvsasa di 80 Uttaraphalgunl of the regnal 
year 11 of Kaniska, was July 18, 1923 ; while the date Sam 6, 
Ghetrasa, mahasa divasea athama di 8, corresponds to March 28, 
1935, From the calendars for these years it is clear that Dr. Van 
Wijk has used the Indian full-moon ending lunar months in place 
of those whicK are directly indicated in the KharostM inscriptions. 
On this point I invite the attention of the reader to the finding of 
Dr. Konow quoted below : 

" We are on safer grounds when we want to ascertain whether 
the months began with' full or firew^raomi. TKe Zeda inscription 
of tKe ye.ar 11 is dated on the 20tK of Asddha, and the naksatra 
is given as Uttaraptialgunl. Prof. Jacobi has kindly informed me 
of the fact that tha.nafe$ara belongs to the Sukla paksa, where it 
may occur between the fifth and the eighth day. If, therefore, the 
twentieth day of the month falls in the beginning of the bright 
half, in our case the fifth day after the new-moon, the full-moon 
day must be the first day of the month. 

The same result can apparently be derived from the 
Takt-i-Bahi inscription, where the first V&tiaklfia, seems to be 
characterised as (puna) paksa, evidently because it was the 
80 1408B 



234 ANCLE NTT INDIA NT CHRONOLOGY 

Buddha's birth-day, which tradition sometimes gives as the 
full-moon of VatidMia." 1 

If the first day of VaiSdkha, was the full-moon day of VaiMkha, 
then what is lunar Vaiakha of the Kharosthl inscriptions would 
end on the day before the full-moon of Jyaistha. SucK a month 
is called in the Hindu calendar, not Vatiakha but Jyaistha. The 
corresponding dates in our own times of tEe 20th" Asadha Sam 11, 
and the 8th of Gaitra of Sam 61 of the inscriptions, which were 
taken respectively as July 18, 1927 and March 28, 1935, would 
show that Dr. Van Wijk has misunderstood the meaning of these 
peculiar lunar .months of the Kharosthl inscriptions. 

.We understand that the earlier era of the Kharosthl inscriptions 
was really Seleucidean era reckoned from the year 311 B.C. The 
era may also be that of Ghandragupta started from the year about 
321 B.C. or it may also be that of Aoka the Great, first 
determined from the year 272 B.C., but started later on from 
267 B.C. It cannot be- Parthian era, as Kaniska's date of 
accession must be very* hear to the year 78 A,D;, and his regnal 
years in all probability started from 80 A.D., the epoch of the 
Paitamahasiddhanta. As to Dr. L'uders's view on this point 
we can say that the donors of the Mathura inscription of the year 
292 may be Greek, but the inscription was made intelligible for 
other people, fli#., the Indian; the era in question may more 
likely be that of Chandragupta or of Asoka the Great. Too 
much overlapping of the two eras is, however, inadmissible. 
The era in question most probably was the Seleacidean era. 



" l Konow's Introduction to Corpus Inscriptionum Indicarum, Vol. II., J>, Ixxxiv. 



CHAPTER XXIY 

INDIAN ERAS 
The Samvat or the Malava Era 

In this chapter it is proposed to discuss three points in 
relation to the Malava or the Samvat era : (i) how it was started 
initially with the mode of reckoning the year, (if) why it is called 
Krta era and (Hi) why in the Malava or the Vikrama Samvat 529, 
on the second day of the lunar month of Tapasya, or Phalguna, 
the Indian season of spring is said to have already set in, as we 
have it in Fleet's Gupta* Inscriptions, Plate No. 18. 

This era, which is at present better known as the Vikrama 
Samvat, has its year-beginning from the light half of lunar 
Gaitra according to the rule of the scientific siddhantas or 
treatises on astronomy, all of "which are of different dates which 
cannot be earlier than 499 A.D. In the preceding chapters, it has 

been shown that from the earliest Vedic times, the year was taken 
to begin from the winter solstice day ; the Veddngas also followed 
the same rule. Tt was perhaps BO, also with Christian era 
initially. We now proceed to discover how this Malava or the 
Samvat era was started initially, on this hypothesis, from the 
winter solstice day, 

Initial Starting of the Era 

Now, 1997 of Samvat era = 1940-41 of the Christian era 
.*. year of Samvat era = 57 of the Christian era 

= 58 B.C. 

From 58 B.C. to 1940 A.D., the mean precession rate was 
50"'G370 per year, and in 1997 years, the total precession of 
the equinoxes and solstices has been - 2745'24" nearly. ^Hence 
what was 270 of the longitude of the sun about 58 B.C., is now 
about 29745'27", which is the present-day longitude of the sun 
about the 19th of January. 



236 ANCIENT INDIAN CHRONOLOGY 

Now, 1997 years = 1939 yrs. + 19x3 years + 1 yr. Hence 
we get an accurate luni- solar cycle of 1996 years. Further 1996 
sidereal years = 729052 days nearly. We apply these days 
backward to Jan. 20, 1939 A.D. and arrive at : 

(1) The date, Dec. 25, 59 B.C., on which at G. M. N., 

Mean Sun '= 270 55' 29"'86, 
,, Moon = 260 54' 57"'65, 
Lunar Perigee = 260 10 ; 8"*99. 

Here the new-moon fell on the the 26th December, and not 
on the .winter solstice day which was the 24th December. It is 
unlikely the Samvat year reckoning had its origin from such a 
new-moon day. 

(2) Secondly a ull-nioou happened on Jan. 19, 1935 A.D. ; 
then by a process similar to that shown above we arrive at : 

The date, Dec. 25, 63 B.C., on which at G. M. N., 

Mean Sun = 270 53' 89* '16, 
Moon 90 12' 12*'27, 
Lunar Perigee = 97 22' 66"'91, 
Sun's Apogee = 67 39' 24"'69. 
,, Eccentricity = '0175223. 

The full-moon no doubt happened on this date, but it was the 
day following the winter solstice. If year-reckoning was started 
on the basis of the correctly ascertained winter solstice day of 
this year, the lunar months would be reckoned to begin from 
the full-moon day of the lunar Pau$a, as in the Kharosthi 
inscriptions, as we shall see later on. The distinguishing 
character of this Pausa was that the full-moon was conjoined 
with the ' junction star ' Punarvasu (/8 Gemniomm) very nearly. 
We, however, try to find the full-moon or the new-moon which 
happened exactly on the winter solstice day, 

(3) We go up by 8 years or 99 lunations from Dec. 26,- 
59 B.C., and arrive at : 

The date, Dec. 24, 67 B.C., on which at GKM.N., 



INDIAN EEAS 287 

Mean Sun = 269 52' 40" '10, 



Mean Moon = 266 18' 52"*09 J 
Lunar Perigee = 294 29' 57" '00, 
Sun's Apogee = 67 35' 19" ' 



The corresponding 
date in our time 
Jan. 19, 1931. 



,, Eccentricity = '017524 

Here the new-moon happened on the day following, i.e., on 
the 25th Dec., the day after the winter solstice. 

(4) We next go up by 8 years or 99 lunations from Dec. 25, 
63 B.C. and arrive at : 

The date Dec. 24, 71 B.C., on which at G.M.N., 



Mean Sun - 269 50' 53"*49, 

Moon= 95 36' 6"'54, 

Lunar- Perigee = 131 43' 18"'00. 



The corresponding 
date in our time 
Jan. 17, 1927. 



Here the full-moon and the sun's reaching the winter solstice 
fell on the same day, and the full-moon was conjoined with the 
* junction star ' of Punarvasu or /3 Gemniomm, and this was the 
distinguishing mark of the winter solstice day. The practice 
was, probably, to intercalate one lunar month occasionally on the 
return of the similar full-moon near ft Gemniorum. This is on 
the assumption that the year was begun from the dark half 
of Pausa. 

(5) Lastly to finally examine if the new-moon and the winter 
solstice fell on the same date, we find that on : 

The date Dec. 23, 75 B.C., at G.M.N., 
Mean Sun=268 49' 67"'16 The corresponding date 



Mean Moon^271 42' 46"'21 
Lunar Perigee=328 49' 58"*00 



in our time 
Jan. 17, 1923 A.D. 



The new-moon happened on this day but it was the day before, 
the winter solstice. 

On the whole it is not impossible to infer that the year of the 
Samvat era used also to be reckoned from the light half of 
Magha, i.e., from a day which was like the new-moon day of 
Jan. 17, 1923 of our time ; the distinguishing character of this 
Magha was that its first quarter was conjoined with /3 Arietts, the 



238 ANCIENT INDIAN CHRONOLOGY 

* junction star * of the naksatm Asvinl. Perhaps the Indian 
orthodox reckoning also started from the light half of the lunar 
Maglia of this type, while the Kharosthl inscriptions have the 
reckoning from the very full-moon day itself of lunar Pausa, with 
the distinguishing feature found in (2) and (4), 

The winter solstice day which just preceded the year 58 B.C., 
was the 24th Dec., 59 B.C. The new-moon near this date fell 
on the 26th. It appears that the Sam vat or rather the Malava 
era did not actually begin with 58 B.C., but most probably from 
57 B.C., and that Sain vat years are not years elapsed, but are> 
like the Christian years, the current ones. This will be clear 
from the next topic dealt with, viz., 

(ti) Why the Samvat Years are called Krta Years. 

The oldest name of the Sarhvat years was also Krta years, as 
has been noticed by all the Indian archaeologists from Dr. Fleet 
up to Dr. D. E. Bhandarkar and others of later times. We 
propose to find the reasons thereof in this part of the chapter. 

(1) According to all Indian Calendars, the Krtayuga began 
(a) on a Sunday which was (b) the third day of the of the lunar 
Vaitiakha and (<?) on which ,the moon was conjoined with the 
Krttikas or Pleiades according to the Purdnas. 

The Matsya Purdna says : 



** God Visnu caused barley to ripen on the third day of the 
light half of lunar VaUaklia and started the Krtayuga. 9 ' 
The same Purdna also says : 



3 



II Ch . 65, 2-3. 

" Those people who have fasted on the third day of the light half 

of lunar Vaiakha, would earn inexhaustible merit for it and for 

all other good deeds. If this day be the one on which the moon 

is conjoined with the Krttikas (Pleiades), it is the most valued of 



INDIAN EEAS 239 

all : whatever be given away either as charity or as oblations to 
the gods, or whatever be done by repeating the prayer, has been 
declared by the wise as of unending religious merit." 

The first signal for the beginning of the Krta era, therefore, 
was that the day should be the third of the light half of lu:,ar 
Vaiakha, should be a Sunday and should also be the day on 
which the moon was conjoined with the Pleiades group. 

The second signal for the beginning of the Krtayuga according 
to the Mahdbhdrata and the Purnnas 1 was : 



" The Krtayuga would begin when the sun, moon, Jupiter 
and the naksatra tisya (Pusya) would come into one cluster 



Astronomically speaking, the condition for both these aspects 
to happen in one year for the beginning of the Krtayuga, 
would not perhaps lead to any single solution; but we are here to 
look for a year near about 57 B.C., in which both these events 
occurred. That year has come out from my investigation to have 
been the year 63 B.C. 

(1) In this year, the lunar Cailra ended on March 20, 63 B.C. 
(a) On this day, at G-. M. N., 



Mean Sun =354 54' 48" '57, 
Moon=360 48'45''*69, 
Lunar Perigee = 66 11' 49"'71, 
Sun's Apogee =67 39' 
,, Eccentrieity= '017522. 



Hence 

Appt. Moon = 3567/ 
,, Sun =35649' 



The new-moon happened at about 6-30 p.m. of Ujjayini 
mean time. 

(6) On March 21, 63 B.C., at G. M. N., 



Mean Sun=355 53' 56"'90, 

,, Moon= 13 53'20"'72, 

Lunar Perigee = 66 18' 80"' 76 



Hence 

Appt. Moon = 10 17' 
Sun =357 48' 



T lie first tithi of the siddhdntas was over about 4 p.m., of 
Ujjayini mean time, and the crescent moon was visible after 
sunset most probably. 

1 Mbh, t Vana, 190, 90-91, 



240 ANCIENT INDIAN CHRONOLOGY 

(c) On Sunday, March 22, 63 B.C. *(J. D. = 1698493), at 

G.M.N., 

Mean Sun =356 58' 4*" 23, 1 Hence 

Moon =27 9' 56* '75, Appt. Moon =24 37', 

Lunar Perigee = 66 25' 11"'81. I- ,, Sun =358 46', 

and the Krttika (r\ Tauri)-Bl 26' nearly. 

The siddhantic second tithi was over at about 1-20 p.m. 
of Ujjayini mean time. According to the state of Hi'idu 
astronomy of that time the second day of the lunar VaiSakha was 
taken to end with the setting of the moon on this Sunday evening, 
and the third day began. Wihen both the moon and the Krttika 
cluster became visible affcer sunset, they were separated by about 
6 of longitude. It could be thus inferred that the moon would 
overtake the Krttikas in about half a day. This was probably 
regarded as the first signal for the beginning of the Krtayuga. 

If we think that the connecting of the day of the week, viz., 
Sunday, in the signal for the Krtayuga to begin, was a later 
addition, we have one further aspect to consider, that on the day 
following, the sun reached the Yemal equinox and this was the 
third day of the light half of Vaisakha. Tais *veat was perhaps 
a more forceful signal for the beginning of the Krtayuga. 

As to a/ very early use of the days of the week in the Hindu 
calendar, we have the following well-known passage in the 
Hitopadeda : 



*n 

" Friend, these strings (of the net) are made of guts ; how 
can I then touch them with my teeth to-day which is a 
Sunday ?" The rule was " No meat on Sundays/' But we can 
not be sure of the date of the Hitopadesa. 

It is thus not quite rational for us to assume that the week- 
days were reckoned in the Hindu caleodar about the year 57 B.C. 
But it is clear that the event of the sun's reaching the vernal 
equinox on the third day of lunar VaiSdkha would be regarded as 
of very special significance for the coming of the Krtayuga. 

(2) Secondly this year, 63 B.C., was perhaps called the 
beginning of the Krtayuga for the coming of another astronomi- 
cal event in it, 



INDIAN ERAS 241 



On June 16, 63 B.C., at G. M. N., we bad- 
Mean Sun = 81 88' 59"'72, Hence 



Moon = 80 20' 8"'16, 

Lunar Perigee = 76 0' 2" '58, 
Sun's Apogee = 67 39', 

Mean Jupiter = 80 52' 26" '87, 

Jupiter's Perihelion =341 34' 32", 
Eccentricity= '0443845. 



Appt, Moon = 80 45' 
., Sun =81 11' 

Jupiter as corrected by the 
equation of apsis, 

= 85 54' 54". 

v Oancri =97 5'. 



Jupiter had set already and the new-moon happened in the 
naksatra Punarvasu ; the Jovial year begun was thus Pausa or 
Mahdpausa. The longitude of the oldest first point of the Hindu 
sphere was about, -6 in this year and consequently the longitude 
of the first point of the Pusya division ^as=8720'. Jupiter was 
very near to this point. It may thus be inferred that the signal 
from Jupiter's position as to the beginning of the Krtaynga 
was taken to occur on this date, viz,, June 16, 63 B.C. 

Again on July 16, 63 B.C., at G.M.T. Ohr.,or exactly one 
synodic month later 



Mean Sun =110 43' 37" '39, 

Moon =109" 2' 21" '48, 

Lunar Perigee 79 17' 13"'71, 

Mean Jupiter 83 19' 3'5"'21. 



Hence 

Appfc. Moon =110 57', 
Sun =109 23', 
Jupiter as corrected by the 



eqn. of ap?is=88 19'. 

On this day also the sun, moon, Jupiter and the naksatra 
Pusya were in the same cluster. This day also most probably 
afforded another signal for the coming of the Krtayuga. Jupiter 
had become heliacally visible about 10 days before. 

If we go forward by 12 lunations from the above date, we 
arrive at July 5, 62 B.C., on which, at G.M.N., 

Mean Sun =100 8' 20"'52, 
,, Moon =100 4' 19" -20, 
Jupiter = 112 47' 44"'98, 
8 Cancri =100 4' nearly. 

Here was another combination of the planets, which might 
have persuaded men that the Krtaynga had begun. 

On the whole it is thus established that both the luni- 
solar, and the luni-solar-Jovial-stellar combined signals for the 
beginning of the Krtayuga, could be observed add estimated 
in the year 63 B.C. In this year the sun's reaching the 
winter solstice happened on Dec. 24, and the full-moon 

311408B 



242 * ANCIENT INDIAN CHEONOLOGY 

day of Pausa was the day following it. The actual starting 
of the Krta, Malava or the Samvat era was mada 5 years later 
from the full-moon day of about the 28th Dec., 58 B.C. 
The Samvat year 1 was thus almost the same as 57 B.C., 
and that the number of the Samvat era represents the current 
year as in the Christian era. Further the lunar months here are 
full-moon ending as originally in the Saka era, as we have seen in 
the preceding chapters. The year was reckoned from the full- 
inoon day of Pausa. In 499 A.D. or some years later than this 
date, the Gaitra-Suklddi reckoning was followed according to the 
rule of iryabhata. But in the Samvat era, we are told that the 
lunar months are still reckoned as full-moon ending, which is 
now a case of a queer combination of opposites. We next turn 
to solve the last problem from the epigraphic source in relation 
to this era. 

Malava Samvat 529, the Second Day of the Light Half of 
Phalguna and the Beginning of Spring 

In Fleet's Gupta Inscriptions, Plate No. 18, it is stated that 
spring had set in on the second day of the light half of Phalguna 
of the Malava Samvat ,529 or 473 A.D. Now the year in our 
time which was similar to 529 of the Malava era was 1932 A.D., 
and the date, to March 9, 1932. Elapsed years till this date 
was=1459 sidereal years = 18046 lunalions= 5320909 days. These 
days are applied backward to March 9, 1932 A.D., and we arrive 
at the date : 

Feb. 15, 473 A.D., on which, at the UjjayinI mean mid- 
night, 



Mean Sun =326 58' 8*'09, 

,. Moon =355 57' 22' '72, 

Lunar Perigee =233 43' 28' / *68, 

Sun's Apogee = 76 46' 14" '81, 

,, Eccentricity ='017323. 



Hence 

Appt. Sun = 328= 48' 24", 



Moon=360 20' 



nearly. 



Now the Indian spring begins, when the sun's longitude 
becomes 330% which happened about 30 hours later, i.e., on the 
17th Feb., 473 A.D. The local conditions probably brought iq 
spring earlier. 



INDIAN EEAS 348 

Again 2*5 days before Feb. 15, 473 AJX, afc Ujjayinl mean 
midnight, or on the 13th February, 473 A.D.. at Ujjayini mean 
midday : 

Mean Sun =324 30' 47"'25, 

Mean Moon =323 0' 55^12, 
Lunar Perigee = 233 26' 46" '04. 

It appears that the new-moon had happened about 3J lira, 
before, and the first visibility of the crescent took place on the 
evening of the next day, the 14th Feb. Thus Feb. 15 was the 
second day of the month, as stated in the inscription. 

We now proceed to consider why there has been an error in 
estimating the beginning of spring, which according to an old 
rule should come 60 days after the winter solstice day. We find 
that 60 days before this date, viz., Feb. 15, or, on : 

Dec. 17, 472 A.D., at Ujjayini mean midday, 

Mean Sun =267 20' 87*, 

Moon =284 48' 4", 

Lunar Perigee=226 59' 5". 

The estimated winter solstice day was thus premature by about 
two days. On this day, the first visibility of the crescent took 
place in the evening. Henfce the second day of the light half of 
Phalguna was the estimated beginning of spring, i.e., 60 days 
later. The new-moon happened on the 16fch December and 
the real winter solstice day was the 19th December. 

This inscription shows that the Gupta era cannot be identi- 
fied with the Samvat era. The point that why or how the 
Malava era came to be called Vikrama Samvat cannot be 
answered from any astronomical data, 

Note -We have here tried to interpret the astronomical 
statement of the Mandasor stone inscription of Kumara Gupta 
and Bandhuvarman. The date of the inscription found here as 
Feb 15 473 A.D., was that of the thorough repair and decora- 
te oUhe In te mP .e * Mand^r W8-H ^ * * 
inscription says that spring has set in. 



CHAPTER XXY 

INDIAN BEAS 
The Gupta Era 

In the present chapter, it is proposed "to determine the 
beginning of the era of the Gupta emperors of northern India. 
Dr. Fleet in his great book Inscnptionum Indicaram, Vol. Ill, has 
published a collection of the Gupta inscriptions. In order to 
verify the dates in those inscriptions he had the assistance of the 
late Mr. S. B. Diksita of Poona, and his calculations led Dr. 
Fleet to conclude that the Gupta era began from 319-21 A.D. 1 
This indefinite statement or inference is not satisfactory. Mr. 
Diksita was also not able to prove that the Gupta and Valabhi 
eras were but one and the same era. 2 Of recent years some have 
even ventured to prove that the Gupta era is to be identified with 
the Swhvat or Malava era. Hence it has become necessary to 
try to arrive at a definite conclusion on this point, viz., the true 
beginning of the Gupta era. 

The tradition about this era is recorded by Alberum, which is 
equivalent to this : From the Saka year, deduct 241, the result is 
the year of the Gupta kings and that the Gupta and Valabhi 
eras are one and the same era. 3 Now the Saka era and the 
Samvat or Malava era are generally taken to begin from the light 
half of lunar Caitra. As has been stated already, it is extremely 
controversial to assume if this was so at the times when these 
eras were started. 

From the earliest Vedic times and also from the Vedanga 
period, we have the most unmistakable evidences to show that 
the calendar year, as distinguished from the sacrificial year, was 

* IPleet- Corpus Inscriptionum Indicarum, Vol. Ill (Gupta Inscriptions), page 127. 
3 S. B. Dlkita, qnMfa ^fiWTO, page 375 (1st Edn.). 

3 Sachau's Alberuni, Vol. II, page 7 " The epoch of the era of the G-uptas 
falls, like that of the Valabha era, 241 years later than the 



INDIAN BRAS 245 

started either from the winter solstice day or from the day 
following it. The so-called Caiira-Suklddi reckoning started the 
year from the vernal equinox day or from the day following it. 
So far as we can see from a study of the history of Indian 
astronomy, we are led to conclude that this sort of beginning the 
year was started by Aryabhata I from 499 A.D. The great fame 
of Aryabhata I, as an astronomer, led all the astronomers and 
public men of later times to follow him in this respect. We 
start with the hypothesis that the Gupta era was originally 
started from the winter solstice day and that initially the year of 
the era more correctly corresponded with the Christian year, 
than with the Caitra-Suklddi Saka year 

Now the year 241 of the Saka era is equivalent to 319-20 A.D. 
We assume that the Gupta era started from the winter solstice 
day preceding Jan. 1, 319 A.D. The elapsed years of the Gupta 
era till 1940 A.D., becomes 1621 years and 1621=160x10+19+2. 
Hence the starting year of the era was similar to 1938 A.D. 
Now the mean precession rate from 319 to 1938 A.D. =50" '0847 
per year. Hence the total shifting of the solstices becomes till 
1938 AJX = 22 31' 27"'54. Thus what was 270 of the longitude 
of the sun, should now become 291 31' nearly a longitude 
which the sun now has about the 13th of January. On looking 
up some of the recent calendars we find that : 

(a) In the year 1922, there was a full-moon on Jan. 13. 
(6) ,, ,, ,, 1937, ,, ,, a new-moon on Jan. 12. 

We apply the elapsed years 1619 (sidereal) backward to 
Jan. 32, 1937 A.D., and arrive at the date : 

Dec. 20, 317 A.D., on which, at G.M.N., or Ujjayim M.T. 
5-4 p.m., 



Mean Sun =269 5' 11"'26, 

Moon =272 89' 40* '40, 

Lunar Perigee =39 50' 37"'26, 
A. Node =257 44' 29 '88, 

Sun's Apogee = 74 7'2516, 
, , Eccentricity = '0173808. 



Hence 2e =119''5016, 

fe 2 =1''2981, 
Appt. Sun =26937'. 
,, Moon 26852' nearly. 



The moon overtook the sun in about 1J hours and the sun 
reached the winter solstice in about 9 hours. Hence Dec. 20, 
317 A.D,, was a new-moon day and also the day of winter solstice 



246 ANCIENT INDIAN CHRONOLOGY 

according to the ordinary mode of Indian reckoning. As this 
day was similar to Jan. 12, 1937 A.D., viz., lunar Agrahdyana 
ended, it appears thai the Gupta era was started from about the 
21st Dec., 318 A.D., and this was the 12th day of lunar Pausa. 
It must be remembered in this connection, that the distinguishing 
character of the lunar Agrahdyana^ with which the year ended at 
the end of a correct luni-solar cycle, was that the last quarter of 
the moon was very nearly conjoined with Citrd (Spica or 
a Virginis) * In our opinion this character of the month was used 
for the intercalation of a lunar month at the end of a correct 
luni-solar cycle. We now proceed to examine the dates given in 
the Gupta Inscriptions as collected together by Dr. Fleet in his 
great book on the subject. 

/. The First Instance of Gupta Inscription Date 



Sri 2 

The inscription says that the 12th tithi of the light half of 
lunar Asddha of the Gupta year 165 fell on a Thursday. We 
examine this by both the modern and the Siddhdntic methods. 

(A) By the Modern Method, 

The year 165 of the Gupta kings is similar to the year 1924 
A.D. The elapsed years till this date =1440 sidereal years== 
525969 days. We increase the number of days by 1 and divide it 
by 7 ; the remainder is 4, which shows that the inscription state- 
ment of Thursday agrees with the Sunday of July 13, 1924 A.D. 

We next apply 525969 days backward to July 13, 1924, and 
arrive at the date June 21, 484 A.D., the date of the inscription. 

This date was 14*15 Julian centuries + 181 '25 days before 
Jan. 1, 1900 A.D. Hence 

On June 21, 484 A.D., at G.M.N., 

Mean Sun = 91 12' 50"'64, Hence 

Moon =235 7' 53'/'42, 2e = 119''0564. 

Lunar Perigee =335 23' 2'/'80, |e 2 = 1''290. 

A. Node =277 14' 51'/'51, 

Sun's Apogee = 76 14' 32", 
Eccentricity = "0173175. 

1 C/. the longitude of the moon on Jan, 4, 1937 A.D , at L. Q. with that of 
a Virginis. 

* ^Fleet's Gupta Inscriptions, page 80, Eran Inscription. 



INDIAN EEAS 247 

From these we readily find the same mean place* at the 
preceding Ujjayinl mean midnight. Hence 

On June 20, 484 A.D., at Ujjayim mean midnight, 
Mean Sun - 90 30' 47" '38, 

Appt. Sun = 90= 2 f , 

,, Moon= 219" 47' nearh . 



Moon =225 45' 41"'78, 

Lunar Perigee =335 18' 17'61, 
A. Node , =277 17' 7"'08. 



Thus at the Ujjayinl mean midnight of the day before 
(Wednesday), the lUh tithi was current, and next day, Thursday. 
had at sun rise the 12th tithi of the lunar month of Isadha. 

(B) According to the method of the Khandakhadyaka of 
Brahmagupta, the Kali ahargana on this Wednesday at the 
Ujjayini mean midnight was= 1309545. Hence 

Mean Sun = 91 3 ; 4" t 

,, Moon = 22623'17"| 

Lunar Perigee =335 42' 56% 

A. Node =277 35' 17".' 

The above two sets of the mean elements for the same instant 
are in fair agreement. Hence the date of the inscription is 
Thursday, June 21, 484 4,D., and the Zero year oj the Gupta 
era is thus 319 A.D. We are here in agreement with Diksita's 
finding. 

IL The Second Instance of Gupta Inscription Date 



Here the Hijn year 662 shows the Vikrama Sam* at is 
expressed in elapsed years as 1320 ; and as it is now reckoned 
it should be 1321. The Valabhi Sariwat 945 is the same as the 
Gupta Sarhvat 945, in which the 13th tithi of the dark half of 
Jyaistha fell on a Sunday. 

Now the mean Khaydakliddyaka ahargana 

= 218878 

from which we deduct 3Q 

211848, 
which we accept as the correct ahargana and is exactly divisible 

i Fleet-Gupta Inscriptions, page 84, Veraval Inscription. 



248 ANCIENT INDIAN CHRONOLOGY 

by 7, and which was true for Saturday of Isddha vadi 12 of the 
Gupta era 945. The English date for this Saturday was May 25, 
1264 A.D. On the next day, Sunday, the date was, May 26, 
1264 A.D., the date of the inscription. 

From the above apparent dhargana for May, 25, 1264 A.D., 
which was a Saturday, at the Ujjayim mean midnight, we have 

Mean Sun = 1 s 27 42' 48", 
Moon = 0* 27 31' 40", 

Lunar Apogee = 6* 20 29' 1* (with Lalla's correction) 
A. Node = 9* 29 53' 4" ( Do. Do. Do ) 
Hence, Appt. Sun = 1* 28 21' 57", 
Moon = s 28 8' 44", 

Moon-Sun =10*29 46' 47" 

5 46' 47". 



Thus at the midnight (U.M.T.) of the Saturday ended, 
about 11 hrs. of the 13th titlii of the dark half of Jyaistha, were 
over and 13 hrs. nearly of it remained. Thus the current titlii 
of the next morning of Sunday was also the 13th of tjie dark 
half of Jyaistha which is called Asddha vadi 13. 

In the present case the Valabhi or Gupta year 945 = 1264 
A.D. Hence also the Gupta era began from 319 A.D,, and we 
are in agreement with Diksita. 

III. The Third Instance of Gupta Inscription Date 



It is here stated that in the Gupta or Valabhi year 927, 
the 2nd titlii of the light half of Phalguna fell on a Monday. 
The English date becomes 1246 A.D., Feb. 19, Saka year 
was 1167 years -h 11 months + 2 tithis, the Gupta year being 
taken to have been reckoned from the light half of lunar Pausa. 

i Fleet's Gupta Inscriptions, page 90, Veraval Inscription. 



INDIAN ERAS 241 



On June 16, 63 B.C., at G-. M. N., we had- 



Mean Sun = 81 38' 59" '72, 

Moon = 80 20' 8"'16, 

Lunar Perigee = 76 0' 2"*58, 
Sun's Apogee = 67 39', 

Mean Jupiter = 80 52' 26"*87, 

Jupiter's Perihelion =341 34' 32", 
,, Eccentricity ='0443845. 



Hence 

Appfc. Moon = 80 45' 
., Sun =81 11' 

Jupiter as corrected by the 
equation of apsis, 

= 85 54' 54". 

v Cancri =97 5'. 



Jupiter had set already and the new-moon happened in the 
naksatra Punarvasu ; the Jovial year begun was thus Pausa or 
Mahdpausa. The longitude of the oldest first point of the Hindu 
sphere was about, -6 in this year and consequently the longitude 
of the first point of the Pusyd division vsas=8720'. Jupiter was 
very near to this point. It may thus be interred that; the signal 
from Jupiter's position as to the beginning of the Krtayuga 
was taken to occur on this date, viz., June 16, 63 B.C. 

Again on July 16, 63 B.C., at G.M.T. Ohr.,or exactly one 
synodic month later 



Mean Sun =110 43' 37" '39, 

,, Moon = 109" 2' 21" '48, 

Lunar Perigee 79 17' 13"'71, 

Mean Jupiter = 83 19' 35" '21. 



Hence 

Appt. Moon = 110 57', 
Sim =109 23', 
Jupiter as corrected by the 



eqn. of apsis=88 19'. 

On this day also the sun, moon, Jupiter and the naksatra 
Pusyd were in the same cluster. This day also most probably 
afforded another signal for the coming of the Krtayuga. Jupiter 
had become heliacally visible about 10 days before. 

If we go forward by 12 lunations from the above date, we 
arrive at July 5, 62 B.C., on which, at G.M.N., 

Mean Sun =100 8' 20" '52, 
Moon = 1004'19"'20, 
Jupiter = 112 47' 44" '98. 
8 Cancri =100 4' nearly. 

Here was another combination of the planets, which might 
have persuaded men that the Krtayuga had begun. 

On the whole it is thus established that both the luni- 
solar, and the luni-solar-Jovial-stellar combined signals for the 
beginning of the Krtayuga, could be observed and estimated 
in the year 63 B,C, In this year the sun's reaching the 
winter solstice happened on Dec. 24, and the full-moon 

31 1408B 



242 ANCIENT INDIAN CHEONOLOGY 

day of Pausa was the day following it. The actual starting 
of the Krta, Malava or the Samvat era was made 5 years later 
from the full-moon day of about the 28th Dec., 58 B.C. 
The Samvat year 1 was thus almost the same as 57 B.C., 
and that the number of the Samvat era represents the current 
year as in the Christian era. Further the lunar months here are 
full-moon ending as originally in the Saka era, as we have seen in 
the preceding chapters. The year was reckoned from the full- 
moon day of Pausa. In 499 A.D. or some years later than this 
date, the Caitra-Sukladi reckoning was followed according to the 
rule of Aryabhata. But in the Samvat era, we are told that the 
lunar months are still reckoned as full-moon ending, which is 
now a case of a queer combination of opposites. We next turn 
to solve the last problem from the epigraphic source in relation 
to this era. 

Malava Samvat 529, the Second Day of the Light Half of 
Phalguna and the Beginning of Spring 

In Fleet's Gupta Inscriptions, Plate No. 18, it is stated that 
spring had set in on the second day of the light half of Phalguna 
of the Malava Samvat 529 or 473 A.D. Now the year in our 
time which was similar to 529 of the Malava era was 1932 AJX, 
and the date, to March 9, 1932. Elapsed years till this date 
was=1459 sidereal years = 18046 lunations -5320909 days. These 
days are applied backward to March 9, 1932 A.D., and we arrive 
at the date : 

Feb. 15, 473 A.D., on which, at the Ujjayin! mean mid- 
night, 



Mean Sun =326 58' 8^09, 

,. Moon =355 57' 22"'72, 

Lunar Perigee =233 43' 28" '68, 

Sun's Apogee = 76 46' 14* '81, 

,, Eccentricity ='017323, 



Hence 

Appt. Sun =328 48' 24', 



Moon=360 20' 



nearly. 



Now the Indian spring begins, when the sun's longitude 
becomes 330, which happened about 30 hours later, i.e., on the 
17th Feb., 473 A.D. The local conditions probably brought in 
spring earlier. 



INDIAN ERAS 248 

Again 2'5 days before Feb. 15, 473 A.D., at Ujjayim mean 
midnight, or on the 13th February, 473 A.D,. at Ujjayiui mean 
midday : 

Mean Sun =324 30' 47"'25, 

Mean Moon =323 0' 55"T2, 

Lunar Perigee = 233 2t>' 46" '04. 

It appears that the new-nioon had happened about 3| hr$. 
before, and the first visibility of the crescent took place on the 
evening of the next day, the 14th Feb. Thus Feb. 15 was the 
second day of the month, as stated in the inscription. 

We now proceed to consider why there has been an error in 
estimating the beginning of spring, which according to an old 
rule should come 60 days after the winter solstice day. We find 
that 60 days before this date, t>fe., Feb. 15, or, on: 

Dec. 17, 472 A.D., at TJjjayini mean midday, 

Mean Sun =267 20' 87*, 

Moon =284 48' 4", 

Lunar Perigee=226 59' 5". 

The estimated winter solstice day was thus premature by about 
two days. On this day, the first visibility of the crescent took 
place in the evening. Hence the second day of the li-ht half of 
Phalquna was the estimated beginning of spring, i.c., 60 days 
later. The new-moon happened on the 16th December and 
the real winter solstice day was the 19th December. 

This inscription shows that the Gupta era cannot be identi- 
fied with the Sa**at era. The point that why or how the 
Malava era came to be called Vikrama &...* cannot be 
answered from any astronomical data, t 

Tot,-We have here tried to interpret the astrononnc 1 

inscription says that spring nas set in. 



CHAPTER XXY 

INDIAN Eli AS 

The Gupta Era 

In the present chapter, it is proposed to determine the 
beginning of the era of the Gupta emperors of northern India. 
Dr. Fleet in his great book Inscriptionum Indicaram,~Vol. Ill, has 
published a collection of the Gupta inscriptions. In order to 
verify the dates in those inscriptions he had the assistance of the 
late Mr. S. B. Diksita of Poona, * and his calculations led Dr. 
Fleet to conclude that the Gupta era began from 319-21 A.D. 1 
This indefinite statement or inference is not satisfactory. Mr. 
Diksita \vas also not able to prove that the Gupta and Valabhi 
eras were but one and the same era. 2 Of recent years some have 
even ventured to prove that the Gupta era is to be identified with 
the Samvat or Malava era. Hence it has become necessary to 
try to arrive at a definite conclusion on this point, viz., the true 
beginning of the Gupta era. 

The tradition about this era is recorded by Alberuni, which is 
equivalent to this: From the Saka year, deduct 241, the result is 
the year of the Gupta kings and that the Gupta and Valabhi 
eras are one and the same era. 8 Now the Saka era and the 
Samvat or Malava era are generally taken to begin from the light 
half of lunar Gaitra. As has been stated already, it is extremely 
controversial to assume if this was so at the times .when these 
eras were started. 

From the earliest Vedic times and also from the Veddnga 
period, we have the most unmistakable evidences to show that 
the calendar year, as distinguished from the sacrificial year, was 

* WeeiCorpus Inscriptionum Indication, Vol. Ill (Gupta Inscriptions), page 127. 

* S. B. Diksita, *TH#ta sstfiwrer, page 375 (1st Edn.). 

3 Sachau's Alberani, Vol. II, page 7" The epoch of the era of the Guptas 
falls, like that of the Valabha era, 241 years later than the Sakdkala." 



INDIAN ERAS 245 

-started either from the winter solstice day or from ^he day 
following it. The so-called Caitra-jSuklddi reckoning started the 
year from the vernal equinox day or from the day following it. 
So far as we can see from a study of the history of Indian 
astronomy, we are led to conclude that this sort of beginning the 
year was started by Aryabhata I from 499 A.D. The great fame 
of Aryabhata I, as an astronomer, led all the astronomers and 
public men of later times to follow him in this respect. We 
start with the hypothesis that the Gupta era was originally 
started from the winter solstice day and that initially the year of 
the era more correctly corresponded with the Christian year, 
than with the Caitra-SuMddi Saka year. 

Now the year 241 of the Saka era is equivalent to 319-20 A.D. 
We assume that the Gupta era started from the winter solstice 
day preceding Jan. 1, 319 A.D. The elapsed years of the Gupta 
era till 1940 A.D., becomes 1621 years and 1621=160x10+19 + 2. 
Hence the starting year of the era was similar to 1938 A.D. 
Now the mean precession rate from 319 to 1938 A.D. = 50" '0847 
per year. . Hence the total shifting of the solstices becomes till 
1938 A.D. = 22 31' 27"*54. Thus what was 270 of the longitude 
of the sun, should now become 291 31' nearly a longitude 
which the sun now has about the 13th of January. On looking 
up some of the recent calendars we find that : 

(a) In the year 1922, there was a full-moon on Jan, 13. 

(b) ,, ,, 1987, ,, a new-moon on Jan. 12. 

We apply the elapsed years 1619 (sidereal) backward to 
Jan. 12, 1937 AJ)., and arrive at the date: 

Dec. 20, 317 A,D., on which, at G.M.N., or Djjaymi M.T. 
5-4 p.m., 



Mean Sun - *=269 5' 11"'26, 

,, Moon = 272 39'40"'40, 

Lunar Perigee =39 50' 37"'26, 

A. Node =25744/29-88, 

Sun's Apogee = 74 7' 25'16, 

, , Eccentricity = '0173808. 



Hence 2e =119''5016, 



Appt. Sun =26937'. 
, , Moon - 2G852' nearly . 



The moon overtook the sun in about 1 hours and the sun 
reached the winter solstice in about 9 hours/ Hence Dec. 20, 
317 A.D., was a new-moon day and also the day of winter solstice 



246 ANCIENT INDIAN CHRONOLOGY 

according to the ordinary mode of Indian reckoning. As this 
day was similar to Jan. 12, 1937 A.D., viz., lunar Agrahdyana 
ended, it appears that the Gupta era was started from about the 
21st Dec., 318 A.D., and this was the 12th day of lunar Pausa. 
It must be remembered in this connection, that the distinguishing 
character of the lunar Agrahdyana, with which the year ended at 
the end of a correct luni-solar cycle, was that the last quarter of 
the moon was very nearly conjoined with Citrd (Spica or 
a Virginia)^ In our opinion this character of the month was used 
for the intercalation of a lunar month at the end of a correct 
luni-solar cycle. We now proceed to examine the dates given in 
the Gupta Inscriptions as collected together by Dr. Fleet in his 
great book on the subject. 

I. The First Instance of Gupta Inscription Date 



The inscription says that the 12th titlii of the light half of 
lunar Isadha of the Gupta year 165 fell on a "Thursday. We 
examine this by both the modern and the Siddhdntic methods. 

(A) By the Modern Method. 

The year 165 of the Gupta kings is similar to the year 1924 
A.D, The elapsed years till this date=1440 sidereal years= 
525969 days. We increase the number of days by 1 and divide it 
by 7 ; the remainder is 4, which shows that the inscription state- 
ment- of Thursday agrees with the Sunday of July 13, 1924 A.D. 

We next apply 525969 days backward to July 13, 1924, and 
arrive at the date June 21, 484 A.D., the date of the inscription. 

This date was 14*15 Julian centuries + 181*25 days before 
Jan. 1, 1900 A.D. Hence 

On June 21, 484 A.D., at G.M.N., 



Mean Sun- = 91 12' 50"'64, 

Moon =235 7' 53" '42, 

Lunar Perigee =335 23' 2"'80, 
A. Node =277 14' 51 "'51, 

Sun's Apogee = 76 14' 32", 
Eccentricity = '0173175. 



Hence 
2e = 119''0564. 
fe 2 =l'-290. 



1 Cf. the longitude of the moon on Jan. 4, 1937 A.D , at L. Q. with that of 
gtnif. 
Fleet's Q-upta Inscriptions, page 80, Bran Inscription. 



INDIAN BRAS 247 

From these we readily find the same mean places at the 
preceding Ujjayini mean midnight. Hence 

On June 20, 484 A.D., at Ujjayini mean midnight, 
Mean Sun 90 80' 47" '38, 



Moon =225 45' 41* '78, 

Lunar Perigee =835 18' 17*61, 
A. Node =277 17' 7" '08. 



Appt. Sun = 90 2', 

M Moon =219 47' nearly. 



Thus at the Ujjayini mean midnight a of the day before 
(Wednesday), the llthtithi was current, and next day, Thursday, 
bad at sun rise the 12th tit hi of the lunar month of Isddha. 

(B) According to the method of the Khandakhadyaka of 
Brahmagupta, the Kali ahargana on this Wednesday at the 
Ujjayini mean midnight was 1309545. Hence 

Mean Sun = 91 3' 4\ 

Moon =226 23' 17^ 

Lunar Perigee =335 42' 56", 

A. Node =277 35' 17*.' 

The above two sets of the mean elements for the same instant 
are in fair agreement. Hence the date of the inscription is 
Thursday, June 21, 484 A. D., and the Zero year of the Gupta 
era is thus 319 A.B, We are here in agreement with Dlksita's 
finding. 

IL The Second Instance of Gupta Inscription Date 



Here the Hijri year 662 shows the Vikrama Samvat is 
expressed in elapsed years as 1320 ; and as it is now reckoned 
it should be 1321. The Valabhi Samvat 945 is the same as the 
Gupta Samvat 945, in which the 13th tithi of the dark half of 
Jyaistha fell on a Sunday. 

Now tbe mean Khanda'khadya'ka ahargana 

= 218878 

from which we deduct 30 

211848, 
which we accept as the correct ahargana and is exactly divisible 

1 Pleefc Gupta Inscriptions, page 84, "Veraval Inscription, 



248 ANCIENT INDIAN CHRONOLOGY 

by 7, and which was true for Saturday of Asadha vadi 12 of the 
Gupta era 945, The English date for this Saturday was May 25, 
1264 A.D. On the nest day, Sunday, the date was, May 26, 
1264 A.D., the date of the inscription. 

From the above apparent aharguna for May, 25, 1264 A,D t , 
which was a Saturday, at the Djjayim mean midnight, we have 

Mean Sun = 1* 27 42' 48", 
Moon = 0*27 81' 40", 

Lunar Apogee = 6' 20 29' 1" (with Lalla's correction) 
A. Node = 9' 29 53' 4" ( Do. Do. Do ) 
Hence, Appt. Sun = 1' 28 21' 57", 
Moon = 0'28 8' 44", 

Moon- Sun =10*29 46' 47" 

= 27 tithis + 5 46' 47". 

Thus at the midnight (U.M.T.) of the Saturday ended, 
abouL 11 hrs. of the 13th tithi of the dark half of Jyaistha were 
over and 13 hrs, nearly of it remained. Thus the current tithi 
of ttte nest morning of Sunday was also the 13th of the dark 
half of Jyaistha which is called Isddha vadi 13. 

In the present case the Valabhi or Gupta year 945 = 1264 
A.D. Hence also the Gupta era began from 319 A.D,, and we 
are in agreement with Diksita. 

III. The Third Instance of Gupta Inscription Date 



It is here stated that in the Gupta or Valabhi year 927, 
the 2nd tithi of the light half of Phalguna fell on a Monday. 
The English date becomes 1246 A.D., Feb. 19, Saka year 
was 1167 years + 11 months + 2 tithis, the Gupta year being 
taken to have been reckoned from the light half of lunar Pausa. 

l Fleet's Gupta Inscriptions, page 90, Veraval Inscription, 



INDIAN ERAS 249 

The true KhandakhaJijka ahargana becomes = 212179 at 
Ujjayini mean midnight of monday, when 

Mean Sun = 10* 24 43' 44", 

Moon = 11* 24 26' 37", 

Lunar Apogee = 6* 3 '20' 53", 

A. Node = 2* 1 59' 40". 

Hence on the same date at 6 a.m., Ujjayini M.T., 

Mean Sun = 10 * 28 59' 23", , __ 
Sun's Apogee = 2< 17 0' 0", lhus ~ 

M TV/T 11. ixo oo; -,, A PP<" Sun = 325 59 ' 2 "> 

Mean Moon = 11* 14 33' 41", hr ,. Ojlft , , ' 

T A ** oc .*, S- M n = S4 2 56' 51". 

Lunar Apogee = 6* 3 C IS' 52" ] ' 

.'. Moon -Sun = 16 57/25" 

57 ; 25", 



On this Monday, the ttthi was the second of the light half of 
unar Phalguna, while the sun's longitude shows that the 
Bengali date was the I 24th of solar Phdlguna. We are here 
in agreement with Dlksita. 

In this case also calculation by the modern methods is 
unnecessary as the time was later than of Brahmagupta. It 
should be noted that the old year-reckoning from the light half 
of Pausa persists inspite of Aiyabhata I's rule of reckoning it 
from the light half of Caitra. Here ako 927 of the Gupta Era 
= 1246 A.D. 

.". Zero year of the Gupta Era = 319 A.D. 

IV. The Fourth Instance of Gupta Inscription Date 



This states that the Gupta year 330 had at its end the second 
Agrahdyana. Here, the Gupta year 330, up to Agraliayana* 
the time by the Caitra-Hukladi Saka era would be 570 years + 
9 months. 

According to the Khandakhddyaka of Brahmagupta, the total 
Kali-solar days up to 570 of Saka elapsed + 9 months = 
1349910, in which we get 1383^ intercalary months, i.e., 
13S3 exact intercalary months by the mean rate, wlrch tends 
to show that there was a se?ond lunar Agrahayana at this time, 
But this explanation appears unsatisfactory. If we follow the 

1 Fleet Gupta Inscriptions, page 92, the Kaira <2245'N, 7245'E) Grunt. 
&J140SB 



250 ANCIENT INDIAN CHEONOLOQY 

method of the Siddhdntas, there can be no intercalary month in 
the Bolar month of Agrahayana, of which the length as found by 
Warren is less than that of a lunar month. 2 We have also 
examined it carefully and found that in the present case this 
could not happen. We have then to examine it another way. 

On Dec. 20 of the year 317 A.D., there was a new-moon 
with which the lunar Agrahdyana ended and the sun turned 
north. The character of this lunar Agrahdyana was that the 
last quarter was conjoined with Citra or a Virginis. The Gupta 
era was started one year later than this date, from the 20th 
Dec.,318A.D. The year 330 of the Gupta era was thus the 
year which ended about Dec. 20, 648 A. D, and the number of 
years elapsed was =331 = 160 x 2 + 1 1 . 

Thus 331 years was a fairly complete lur.i-solar cycle, and 
comprised 120898 days. Again 577825 days before Jan. 1, 
1900 A.D., was the date Dec. 20, 317 A.D. Hence applying 
120898 days forward to this date, we arrive at the date Dec. 20, 
648 A.D., on which the new-moon happened with which the 
lunar Agrahdyana ended this year. 

Now on the day of the last quarter of this month or the 
astaM which fell on the 13th Dec., 648 A.D., the moon was 
conjoined with Gitrd or a Virginis, in the latter part of the 
night. 

On this day, at G. M. N., we had 



Mean Sun =204 57' 0"*47, 

Moon =180 14' 22* '10, 

Lunar Perigee =188 32' 34"'17, 

Sun's Apogee = 79 46' 40"'79. 

2e=118''7, 5e 2 = : 



Hence 

Apparent Sun -265 8'. 
Moon =179 10', 
Long, of a Virgini s = 185 neaily 

From these calculations it follows that the last lunar month 
of the year, was the second Agrahdyana as this month completed 
the luni-solar cycle of 331 years. 

The date of the inscription, being the second day of the 
second Agrahdyana, was the 22nd oj November, 64$ A.D. 
With this second Agrahdyana which ended on the 20th Dec., 

8 Length of Solar Agialiajana=ZQda. 30n. S4v. 2 1 * 1 33 IV (Burgess S. Siddlianta, 
xiv, 8). 

Length of Lunar month =29da. 31n. 50v. 6 I1[ i 53 (ace, to the Khan<}akhadyaka) t 



INDIAN ERAS 251 

648 A.D. , the year 330 of the Gupta era ended. It niu*>l It, 
admitted that the inscription as it has been tead or as it u'tia 
executed was slightly defective. In this case also Anjalhatti Vs 
Caitra-tfukladi reckoning is not followed. 

Here 330 of the Gupta era = 649 A.D. 
.'. Zero of the ,, =319 A.D. 

V. Mom Copper Plate Inscription 



u 



This inscription says that on the day of the 5th tithi of the 
light half of lunar Phalguna of the Gupta year 585, the king of 
the place Morvi (22 49' N and 70 53' B) made a gift at the time 
of a solar eclipse, which happened some time before this date, on 
which the deed of gift, s, the copper plate in question, was 

executed. . , 

To find the date of this copper plate, had been a pit-fall for 
Dr Fleet, ^ho mistook that the solar eclipse in question 
happened on the 7th May, 905 A.D. Now the year 585 of the 
Gopta should be 904 A.D. and the date of execution cf the plate 
should be Feb. 20, 904 A.D. We looked for the solar ^ echp* * 
two lunations, 5 days before and 8 lunat,o C s+o ays before ah 
date Although there happened the two solar ebbp*. at the*. 

^ reckoned not 



according to Aryabhata I s rule. 

era=8-26ofthe Caitra-M ** Jj -^ ^te' of the 

Zero year of the ^ **-**** ^ and the elaijsed 



Dikita did actually find it. 



252 ANCIENT INDIAN CHRONOLOGY 

Nov. 10, 904 A.D., 1 on which, at G-.M.N. or 4-44 p.m. Morvi 

time, 

Mean Sun =234 22' 29"'34, 
Sun's Apogee = 83 9' 18"'32, 
MeanMoou =231 1' 21"*80, 
D. Node =246 7' 31"10, 

Lunar Perigee- 162 10' 10"'68. 

The new-moon happened at mean noon Morvi time, the 
magnitude of the eclipse as visible at the place was about *075. 
The beginning of the eclipse took place at 11-35 a.m. Morvi time, 
the end came about 12-45 noon Morvi mean time. Duration was 
about 1 hr. 10 niin. 1 

Secondly, if we use the Kliandakliadyaka, constants, the 
ahargana becomes for 826 of Saka era + 8 lanations=87528. 
Hence the mean places with Lalla's corrections thereto, at 
G.M.N. at the same day, become: 

Mean Sun =228 18' 5*, 

Moon =224 27' 36", 

D. Node =239 44' 56", 

Lunar Perigee =155 69' 47". 

It appears that this eclipse could be predicted by the method 
of tbe Khandakhadyaha. The gift made by tbis copper plate was 
probably a reward to the calculator of the eclipse. 

VI. Tlie Sixth Instance of Gupta Inscription Date 



Hl I 2 

In the year 156 of the Guptas, which was the Jovial, year 
styled the Malid-vaisakJia year, the inscription records the date as 
the day of the 3rd iithi of the hght half of Kdrtika. 

Now 156 of the Gupta era =475 A.D. 

Julian days on Jan. 1, 475 A.D. =1894552, and 

1900 A.D. =2415021. 

Tbe difference is 520469 days which comprise 14"24 Julian 
centuries +253 days. We incrf-ase 520469 day by 12*25 days and 

1 The above circumstances of the eclipse have beeu calculated by my collaborator, 
Mr. N. C. Lahiri, M.A. 

2 Fleet Gupta Inscriptions, page 104, the Kh6h Grant. 



INDIAN ERAS 253 

arrive at the date, Dec. 20, 474 A.D., on which, at G.M.T.6 hrs. 
or 11-4 a.m. Ujjayim M.T., 

Mean Jupiter =170 54' 6".57, 
Mean Sun = 269 47' 1F.66. 

Henoe we calculate that mean Jupiter and mean Sun became 
nearly equal 289 days later, i.e., on the 17th September, 475 
A.D., at 6 a.m. G.M.T., 

Mean Jupiter = 194 55' 34" '42, 
Mean Sun = 194 88' 19"*15. 

It is thus seen that the mean places would become almost 
equal in 6 hrs. more. For the above mean places, however, 
the equations of apsis for Jupiter and Sun were respectively 
-2 6' 4* -01 and -1 45' 2"-70. Hence their apparent places 
became as follows : 

Appt. Jupiter = 192 49' 30"'41, 
Sun = 192 58' 16* '"45. 

Thus they were very nearly in conjunction at 6 hrs. G.M.T. 
on the 17th September, 475 A.D. 

According to Brahmagupta, Jupiter rises on the east on 
getting at the anomaly of con junction of 14. This takes place 
in 15'5 days. Hence the date for the heliacal rising of Jupiter 
becomes the 2nd October, 475 A.D,, at G.M.T. 18 hrs., when 

Appt. Sun =208 45', and 
,, Jupiter =196 20' nearly. 

.Thus Jupiter was heliacally visible about Oct. 20, 475 A.D. 
The actual date of the inscription was Oct. 18, 473 A.D. 

Here on the day of the heliacal visibility, the sun 
was in the naksatra Vi&Skha., but Jupiter w,as 3 40' behind the 
first point of the naksatra division, the Vernal Equinox of 
the year being taken as the first point of the Hindu sphere. 
According to the rule of naming Jupiter's years as given in 
the modern Surya Siddhanta, XIV, 16-17, it was sun's naksatra, 
on the new-moon prior to October 18, 475 A.D.. the date of the 



254 ANCIENT INDIAN CHRONOLOGY 

inscription, which took place on Oct. 15-1(5 of the year, gave 
the name of the year. The sun would reach the naksatra 
Anurddh a, and the year begun was consequently Mahd vaisdklia 
year of Jupiter. 

This inscription also shows that the Gupta era began from 
319 A.D. 

VII. The Seventh Instance of Gupta Inscription Date 



The inscription records the date as the year 163 of the Gupta 
kings, the Jovial year called Malid Atvayuja, the day of the 
2nd tithi of the light half of Gaitra. 

The year 163 of the Gupta era or 482 A.D. was similar to the 
year 1941 A.D., and the date to March 30, 1941 A.D. In 1459 
sidereal years (1941-482 = 1459), there are 532909 days, which 
are applied backward to the 30th March, 1941 A.D., and we 
arrive at the tentative date of the inscription as March 8, 482 
AJD. On this date, afc G.M.N., we bad- 

Mean Jupiter = 29 58' 8'/'24, 
Sun = 347 12' 47*11. 

Here, Jupiter's heliacal setting is yet to come in about 
30 days. Hence on April 7, 482 A.D., 

Mean Jupiter = 32 27' 46"'22, 

Sun = 16 46' 57"'02 at G.M.N. 

Thus the heliacal setting of Jupiter took place in two days 
more according to Brahmagupta'e rule on the 9th April, 482 
A.D., and the new-moon happened on the 5th April, 482 A.D,, 
when the sun was in the naksatra Bharani. Hence the year to 
come got its name Atvayuga year. But the tentative date of 
the inscription was obtained as March 8, 482 A.D , which was 
21 days before the new-nioon on about the oth April, 482 A.D. 
This needs elucidation. 

' l Fieetr-Gupta Inscriptions, page 110, the Kb&b Grant II 



INDIAN ERAS 255 

Here by coming down by 30 days we arrive at the lunar 
month of Vaisdklia as it is reckoned now. But in the year 482 
A.D., i.e., 17 years before the year 499 A.D., when the Hindu 
scientific siddhantas came into being, the calendar formation 
rule was different. In our gauge year 1941 A.D. the moon of 
last quarter got conjoined with Citrd or a Virginis, on the 20th 
Jan, before sunrise. Hence as pointed out before in this gauge 
year 1941 A.D. also, the lunar Agrahayana of the early Gupta 
period ended on the 27th Jan., 1941 A.D. Thus the lunar month 
that is now called Pausa, in 1941 A.D. was called Agrahayana in 
482 A.D. Hence the lunar Caitra of 482 A.D. is now the 
lunar Vaisakha of 1941 A.D. 

The date of this inscription is thus correctly obtained as the 
7th April, 482 4.D.; the Jovial year begun was a Mahd 
Asvayuja year. This instance also shows that the Zero year 
of the Gupta era was approximately the same as the Christian 
year 319 A.D. 

VI IL The Eighth Instance of Gupta Inscription Date 



(l^Ll) 



This inscription records the date, as the year 191 of the 
Gupta emperors, the Jovial year of Maha-caitra, the day of the 
third tithi of the dark half of lunar Magha. 

We first work out the date on the hypothesis that the Gupta 
jear was in this case also reckoned from the light half of lunar 
Pausa. The Gupta year 191, on this hypothesis, would be similar 
to the Christian year 1931, and the date of the inscription would 
correspond with March 6, 1931 A D, Now this Gupta year 
191-510 A.D., would be later tlan the time of Aryabhata I, 
viz., 499 A.D., by 11 years. 

The elapsed years (sidereal) are 1421, which comprise 17576 
lunations= 519029 days. These days are applied backward to 
the date, March 6, 1931 A.D., and we arrive at the date. Feb. 
12, 510 A.D. 

1 Fleet Gupta Inscriptions, page 114, the Majligavam Grant. 



#56 ANCIENT INDIAN CHRONOLOGY 

On this date, Feb. 1*2, 510 A,D,, at G.M.N,, we bad- 

Mean Jupiter = 158 8' 3"'87. 
Sun = 323 46' 13"*72. 

We find easily the sun and Jupiter had reached equality in 
aiean longitude in 133*5 days before, when, at G.jVLT. far., 

Mean Sun = 142 54' 15'/'50 
Mean Jupiter =F 142 52' 48*57. 

If these were the longitudes as corrected by the equations of 
apsis, than the heliacal visibility would come accorJing to the 
rule of Brahmagupta about 15*5 days later, The mean longitudes 
15,5 days later become 

For Sun = 158 10' 54"'2L 
For Jupiter = 144 10' 7'"25. 

Theses corrected by the equations of apsis, become 

For Sun = 156 3' 27*, 
For Jupiter = 146 16' 41. 

Hence the true heliacal visibility would come in 4 days more, 
We have here (1) gone up by 183*5 days and (2) come down 
by 15*5 days. On the whole we have gone up by 168 days or 5 
lunations -f 21 tithis. Thus on the day of the heliacal visibility 
of Jupiter, which came in four days more, we would have to go 
up by 164 days=5 lunations +17 tithis. This interval we have to 
apply backward to the llth tithi of Mdyha, and we arrive at the 
first day of BMdrapada. The date of the heliacal visibility would 
thus be Sep. 1, 509 A,D., and at G.M.N. the sun's true longitude 
would be 160 9' nearly, which shows that the sun would reach 
the Hastd division. On the preceding day of the new-moon, the 
sun would he ; n the naksatra U. Phalgitni, and the Jovial year 
begun would be styled Phdlguna or the Maha-phalguna year. 
This result does not agree with the statement of the inscription. 

It now appears that after the year 499 A.D. or Xryabhata Fa 
time, the reckoning of the years of the Gupta era was changed 
from the light half of Pausa to the light half of Caitra, according 
to Aryabhata 1's rule : 



\ 

Kalakriya, 31. 



INDIAN ERAS 249 

The true KhandakhaJyka uhargann becomes = 212179 at 
Ujjayini mean midnight of monday, wheu 

Mean Sun = 10* 24 43' 44", 

Moon = 11* 24 26' 37", 

Lunar Apogee - 6* 3 '20' 53", 

. A. Node = 2 5 1 59' 40". 

Hence on the same date at 6 a.m., UjjayinI M.T M 

Mean Sun = 10 s 23 59' 28*. 

' Thus 



IS- 



Sun's Apngee = 2 5 17 0' 0", 

Mean Moon = 11- 14' 33' 41", Appl " Sun - 825 59/ 2 "> 
Lunar Apogee^ 6' 3 16' 52" - Moon = 342 86*51*. 

.'. Moon-Sun = 16 57' 25" 

= ltfc + 4 57/25". 

On this Monday, the tithi was the second of the light half of 
unar Phalguna, while the sun's longitude shows that the 
Bengali date was the 24th of solar Phalgiina. We are here 
in agreement with Dlksita. 

In this case also calculation by the modern methods is 
unnecessary as the time was later tbaa of Brahmagupta. It 
should be noted that the old year-reckoning from the light half 
of Pausa persists inspite of Sryabhata I's rule of reckoning it 
from the light half of Caitra. Here also 927 of the ' Gupta Era 
= 1246 A.D. 

.". Zero year of the Gupta Era = 319 A.D. 

IV. The Fourth Instance of Gupta Inscription Date 



U 55 *W fit^HHi ^ ^ I 1 

This states that the Gupta year 330 had at its end the second 
Agrahdyana. Here, the Gupta year 330, up to Agrahayana, 
the time by the Caitm-Siikladi Saka, era would be 570 years -t- 
9 months. 

According to the Khandakhadyaka of Brahmagupta the total 
Kali-solar days up to 570 of Saka, elapsed + 9 months = 
1349910, in which we get 1383^% intercalary months, i.e., 
1383 exact intercalary months by the mean rate, wh ; ch tends 
to show that there was a second lunar Agrahayana at this time. 
But this explanation appears unsatisfactory. If we follow the 

1 Fleet Gupta Inscriptions, page 92, the Kaira (2245'N, 7245'E> Grant. 



250 ANCIENT INDIAN CHRONOLOGY 

method of the Siddlidntas, there can be no intercalary month in 
the solar month of Agrahdyana, of which the length as found by 
Warren is less than that of a lunar month. 2 We have also 
examined it carefully and found that in the present case ibis 
could not happen. We have then to examine it another way- 

On Dec. 20 of the year 317 A.D., there was a new-moon 
with which the lunar Agrahdyana elided and the sun turned 
north. The character of this lunar Agrahdyana was that the 
last quarter was conjoined with Citrd or a Virginis. The Gupta 
era was started one year later than this date, from the 20th 
Dec,, 318 A.D. The year 330 of the Gupta era w.as thus the 
year which ended about Dec. 20, 648 A.D, and the number of 
years elapsed was =331 = 160x2 + 11. 

Thus 331 years was a fairly complete lur.i-solar cycle, and 
comprised 120898 days. Again 577825 days before Jan. 1, 
1900 A.D. , was the date Dec. 20, 317 A.D, Hence applying 
120898 days forward to this date, we arrive at the date Dec. 20, 
648 A.D., on .which the new-raoon happened with which the 
lunar Agrahdyana ended this year. 

Now on the day of the last quarter of this month or the 
astakd which fell on the 13th Dec,, 648 A.D., the moon was 
conjoined with Ultra or a Virginis, in the latter part of the 
night. 

On this day, at G. M. N., we had 



Hence 

Apparent Sun =265 8'. 
Moon = 179 10', 



Mean Sun =204 57' 0"'47, 

Moon =180 14' 22" 10, 

Lunar Perigee =188 32' 84*17, 

Sun's Apogee = 79 46' 40 /; 79. Long, of a Virginia = 185* neatly 
2e = 118'*7, fe 2 =l''398. 1 

From these calculations it follows that the last lunar month 
of the year, was the second Agrahdyana as this month completed 
the luni-solar cycle of 331 years. 

The date of the inscription, being the second day of the 
second Agrahayana, was the S2nd oj November,- 643 A.D. 
With this second Agrahdyana which ended on the 20th Dec., 



2 Length of Solar AgtaMyana = %Qda. 30n. 24v. 2 rn 33 IV (Burgess S. Siddhanta, 
xiv, 8). 

length of Lunar month =29tfo. Bin, SOv. G"i 53 1 (ace. to the Kharttfakhadyaka), 



INDIAN EKAS 251 

648 A.D., the year 330 of the Gupta era ended. It must be 
admitted that the inscription as it lias been read or as it was 
executed was slightly defective. In this case also Iryabhata I's 
Caitra-Sukladi reckoning is not followed. 

Here 3SO of the Gupta era=649 A.D. 
.'. Zero of the ,, ,, -319 A.D. 

V. Morvi Copper Plate Inscription 



This ins?ription says that OQ the day of the 5th tithi of the 
light half of lunar Phalguna of the Gupta year 585, the king of 
the place Morvi (22 49' N and 70 53' E) made a gift at the time 
of a solar eclipse, which happened some time before this date, on 
which the deed of gift, viz., the copper plate in question, was 
executed. 

To find the date of this copper plate, had been a pit- fall for 
Dr. Fleet, who mistook that the solar eclipse in question 
happened on the 7th May, 905 A.D. Now the year 585 of the 
Gupta should be 904 A.D. and the date of execution of the plate 
should be Feb. 20, 901 A.D. We looked for the solar eclipse, 
two lunations + 5 days before and 8 lunations + 5 days before this 
date. Although there happened the two solar eclipses at these 
times, they were not visible in India. 

We find, however, that here the Gupta year is reckoned not 
from the light half of Pausa>, but from the light half of Caitra 
according to Aryabhata I's rule. Here the year 585 of the Gupta 
era=826of the Caitra-Sukladi Saka era =904-905 A.D., or the 
Zero year of the Gupta era = 319-20 A.D. the date of the 
inscription corresponds to March 3, 1941 A.D., and the elapsed 
years till this date-1036 years = 12814 lunations =378405 days. 
The date of the copper plate works out to have been Feb. 12, 905 
A.D. The eclipse referred to in the inscription happened on 

1 Finally accepted by Fleet Indian Antiquary, Nov., 1891, page 382. 8. B* 
did actually find it. 



AXCIEJTT INDIAN CHRONOLOGY 

Nov. 10, 904 A.D,, 1 on which, at G.M.N. or 4-44 p.m. Morvi 

time, 

Mean Sun =234 22' 29* '84, 
Sun's Apogee = 83 9' 18"'32, 
Mean Moon =231 7' 21* '80, 
D. Node =246 7' 31"'10, 

Lunar Perigee = 162 10' 10"'68. 

The new-moon happened at mean noon Morvi tirae, the 
magnitude of the eclipse as visible at the place was about '075. 
The beginning of the eclipse took place at 11-35 a.m. Morvi time, 
the end came about 12-45 noon Morvi mean time. Duration was 
about 1 hr. 10 mio. 1 

Secondly, if we use the Khatiddkhadyaka constants, the 
ahargana becomes for 826 of Saka era + 8 luuations=87528. 
Hence the mean places with Lalla's corrections thereto, at 
G.M.N. at the same day, become: 

Mean Sun =228 18' 5", 

Moon =224 27' 36", 

D. Node =239 44' 56*, 

Lunar Perigea =155 59' 47". 

It appears that this eclipse could be predicted by the method 
of the Khandakhddyaka. The gift made by this copper plate was 
probably a reward to the calculator of the eclipse. 

VI. Tlit, Sixth Instance of Gupta Inscription Date 



jPn I 

In the year 156 of the Guptas, which was the Jovial year 
styled the Mdlia vaialsha year, the inscription records the date as 
the day of the 3rd Lithi of the light half of Kartika. 

Now 156 of the Gupta era =475 A.D. 

Julian days on Jan. 1, 475 A.D. = 1894552, and 

,, 1900 A,D. =2415021. 

Tne difference is 520469 days which comprise 14'24 Julian 
centuries 4- 253 days. We increase 520469 days by 12*25 days and 

1 The above circumstances of the eclipse have been calculated by my collaborator, 
Mr. N. 0. Lahiri, M.A. 

* Fleet Gupta Inscriptions, page 104, the Khdh Grant. 



INDIAN Ell AS 258 

arrive at the date, Dec. 20, 474 A.D., on which, at G.M.T.6 lu-s. 
or 11-4 a.m. Ujjayim M-T., 

Mean Jupiter =170 54' 6".57, 
Mean Sun =269 4T 11".66/ 

Hence we calculate that mean Jupiter and mean Sun became 
nearly equal 289 days later, i.e., on the ] 7th September, 475 
A.D., at 6 a.m. G.M.T., 

Mean Jupiter = 194 55' 34"'42, 
Mean Sun = 194 38' 19"'15. 

It is thus seen that the mean places would become almost 
equal in 6 hrs. more. For the above mean places, however, 
the equations of apsis for Jupiter and Sun were respectively 
-2 6' 4"'01 and -145'2"'70. Hence, their apparent places 
became as follows : 

Appt. Jupiter = 192 49' 30"'41, 
Sun = 192 53' 16"'45. 

Thus they were very nearly in conjunction at f> hrs. G.M.T. 
on the 17th September, 475 A.D. 

According to Brahinagupta, Jupiter rises on the east on 
getting at the anomaly of conjunction of 14. This takes place 
in 15'5 days. Hence the date for the heliacal rising of Jupiter 
becomes the 2nd October, 475 A.D., at G.M.T. 18 hrs., when 

Appt. Sun =208 45', and 
,, Jupiter =196 20' nearly. 

Thus Jupiter was heliacally visible about Oct. 20, 475 A.D. 
The actual date of the inscription was Oct. 18, 475 A.D. 

Here on the day of the heliacal visibility, the sun 
was in the naksatra VisaWia, but Jupiter was 3 40' behind the 
first point of the naksatra division, the Vernal Equinox of 
the year being taken as the first point of the Hindu sphere. 
According to the rule of naming Jupiter's years as given in 
the modern Surya Siddhdnta, XIV, 16-17, it was sun's naksatra , 
on the new-moon prior to October 18, 475 A.D.. the da/te of the 



254 ANCIENT INDIAN CHRONOLOGY 

inscription, which took place on Oct. 15-lfi of the year, gave 
the name of the year. The sun would reach the naksatra 
Anuradha, and the year begun was consequently Mahd vatidkha 
year of Jupiter. 

This inscription also shows that the Ghipta era began from 
319 A.D, 

VII. The Seventh Instance of Gupta Inscription Date 



The inscription records the date as the year 163 of the G-upta 
kings, the Jovial year called Mahd Ifoayuja, the day of the 
2nd tithi of the light half of Caitra. 

The year 163 of the Gupta era or 482 A.D. was similar to the 
year 1941 A JX, and the date to March 30, 1941 A.D. In 1459 
sidereal years (1941-482 = 1459), there are 532909 days, which 
are applied backward to the 30th March, 1941 A.D., and we 
arrive at the tentative date of the inscription as March 8, 482 
A.D. On this date, at G.M.N., we bad- 

Mean Jupiter = 29 58' 8* '24, 
Sun = 347 12' 47" 11. 

Here, Jupiter's heliacal setting is yet to corne in about 
30 days. Hence on April 7, 482 A.D., 

Mean Jupiter = 32 27' 46"'22, 
, r Sun = 16 46' 57"'02 at G.M.N. 

Thus the heliacal setting of Jupiter took place in two days 
more according to Brahrnagupta's rule on the 9th April, 482 
A.D,, and the new-moon happened on the 3th April, 482 A.D., 
when the sun was in the naksatra Bhamnl. Hence the year to 
come got its name Asvayuga year. But the tentative date of 
the inscription was obtained as March 8, 482 A.D , which was 
21 days before the new-moon on about the 5th April, 482 A.D. 
This needs elucidation. 

i Fleet G-npta Inscriptions, page HO, the ^h6h Grant It 



INDIAN ERAS . 255 

Here by coming down by 30 days we arrive at the lunar 
month of VaiSaklia as it is reckoned now. But in the year 482 
A.D., i.e., 17 years before the year 499 A.D., when the Hindu 
scientific siddhantas came into being, the calendar formation 
rale was different. In our gauge year 1941 A.D. the moon of 
last quarter got conjoined with Citrd or a Virginis, on the 20th 
Jan. before sunrise Hence as pointed out before in this gauge 
year 1941 A.D. also, the lunar Agrahayana of the early Gupta 
period ended on the 27th Jan., 1941 A.D. Thus the lunar month 
that is now called Paiisa in 1941 A.D. was called AgraMyana in 
482 A.D. Hence the lunar Caitra of 482 A.D. is now the 
lunar VaUdkha of 1941 A.D. 

The date of this inscription is thus correctly obtained as the 
Vtli April, 482 A.D.] the Jovial year begun was a Mahd 
Asvayuja year. This- instance also shows that the Zero year 
of the Gupta era was approximately the same as the Christian 
year 319 A.D. 

VIII. The Eighth Instance of Gupta Inscription Date 
8^1*1^ ^Ttji 

i l 



This inscription records the date, as the year 191 of the 
Gupta emperors, the Jovial year of Maha-caitra, the day of the 
third tithi of the dark half of lunar Magha. 

We first work out the date .on the hypothesis that the Gupta 
year was in this case also reckoned from the light half of lunar 
Pausa. The Gupta year 191, on this hypothesis, would be similar 
to the Christian year 1931, and the date of the inscription would 
correspond with March 15, 1931 A D. Now this Gupta year 
191=510 A.D., would be later tl an the time of Aryabhata I, 
viz., 499 A.D., by 11 years. 

The elapsed years (sidereal) are 1421, which comprise 17576 
lunations= 519029 days. These days are applied backward to 
the date, March 6, 1931 A.D., and we arrive at the date. Feb. 
12, 510 A.D. 

1 PJeet Gupta Inscriptions, page 114, the Majligavta Grant. 



256 - ANCIENT INDIAN CHROSTOLOQ-Y - 

On this date, Feb. U, 510 A.D., at G.M.N., we bad- 

Mean Jupiter = 158 8' 8* '87. 
Sun = 828 46' 18* '72. 

We find easily the sun and Jupiter had reached equality in 
mean' longitude in 133 '5 days before, when, at GLM.T. hr., 

Mean Sun = 142 54' 15' '50 
Mean Jupiter = 142 52' 48*57. 

If these were the longitudes as corrected by the equations of 
apsis, then the haliacal visibility would come according to the 
rule of Brahmagupta aboui 15*5 days later. The mean longitudes 
15.5 days later become 

For Sun = 158 HX 54" '21. 
For Jupiter = 144 10' 7'"25. 

Theses corrected by the equations of apsis, become 

For Sun = 156 B f 27', 
For Jupiter = 14(5 l& 41. 

Hence the true heliacal visibility would come in 4 days more. 
We have here (1) gone up by 183 '5 days and (2) come down 
by 15*5 days. On the whole we have gone up by 168 days or 5 
lunations +21 tithis. Thus on the day of the heliacal visibility 
of Jupiter, which came in four days more, we would have to go 
up by 164 days =5 lunations +17 tithis. This interval we have to 
apply backward to the llth tithi of Magha, and we arrive at the 
first day of Bhadrapada. The date of the heliacal visibility would 
thus be Sep. 1, 509 A.D., and at fl-.M.N. the sun's true longitude 
would be 160 9' nearly, which shows that the sun would reach 
the Hastd division. On the preceding day of the new-moon, the 
sun would be ; n the naksatra U. Phalguni, and the Jovial year 
begun would be styled Phalguna or the Maha-phalguna year. 
This result does not agree with the statement of the inscription. 

It now appears that after the year 499 A.D. or Aryabhata I's 
time, the reckoning 01 the years of the Gupta era was changed 
from the light half of Paiisa to the light half of Caitra, according 
to Iryabhata I's rule : 



Kdlakriya, 11. 



INDIAN ERAS 249 

The true KhandakhaJ yka ahargana becomes = 212179 at 
Ujjayim mean midnight of monday, when 

Mean Sun = 10* 24 48' 44", 

Moon = II 4 24 26' 37", 

Lunar Apogee =6*3 20' 53", 

A. Node = 2* 1 59' 40*. 

Hence on the same date at 6 a.m., Ujjaymi M.T., 

Mean Sun = 10* 23 59' 23", _ 

Sun's Apogee = 2* 17 0' 0", - US "~ 

TV/T nr - , , , , o rt , ,,, Appl. Sun = 325 59' 2", 

Mean Moon = 11* 14 33' 41", , f ftjft Af 

T A s QC ,/ o* > Moon = 342 56 51 "- 

Lunar Apogee = 6 s 3 C 15' 52" * 

.'. Moon-Sun = 16 57' 25" 

57' 25". 



On this Monday, the tithi was the seconrl of the light half of 
unar Phalguna, while the sun's longitude shows that the 
Bengali date was the k ^4th of solar Phalguna. We are here 
in agreement with DIksita. 

In this case also calculation by the modern methods 5s 
unnecessary as the time was later than of Brahrnagupta. It 
should be noted that the old year-reckoning from the light half 
of Pausa persists inspite of Aryabhata I's rule of reckoning it 
from the light half of Caitra. Here also 927 of the Gkipta Bra 
= 1246 A.D. 
.'. Zero year of the Gupta Era = 319 A, D. 

IV. The Fourth Instance 0} Gupta Inscription Date 



35 && Giwlte gf? * i 1 

This states that the Gupta year 330 had at its end the second 
Agralwyana. Here, the Gupta year 330, up to Agrahayana, 
the time by the Caitm-8u'klddi Saka era would be 570 years + 
9 months. 

According to the Khandakhadyaka of Brahmagupta the total 
Kali-solar days up to 570 of Saka elapsed + 9 months = 
1349910, in which we get 1383^ intercalary months, i.e., 
1383 ex ict intercalary months by the mean rate, which tends 
to show that there was a second luaar Agrahayana at this time. 
But this explanation appears unsatisfactory. If we follow the 

i Fleet Gupta Inscriptions, page 92, the Kfcira (2245 / N, 7245'E) Grant. 



250 ANCIENT INDIAN CHRONOLOGY 

method of the Siddhantas there can be no intercalary month in 
the solar month of Agrahayana t of which the length as found by 
Warren is less than that of a lunar month* 2 We have also 
examined it carefully and found thai in the present case ibis 
coald not happen. We have thon to examine it another way- 

On Dec. 20 of the year 317 A D. } tture was a new-inoon 
with which the lunar Agrahayana ende-1 and the sun turned 
north. The character of this lunar Agrahayana was that the 
last quarter was conjoined with Oltra or a Virginis. The Gupta- 
era was started one year later than this date, from the 20th 
Dec., 318 A. D. The j ear 330 of the Gupta era was thus the 
year which ended about Dec. 20, 648 A.D. and the number of 
years elapsed was =331 = 160x2 + 11. 

Thus 331 years was a fairly complete lur.i-solar cycle, and 
comprised 120898 days. Again 577825 days before Jan. 1, 
1900 A.D., was the date Dec. 20, 317 A.D. Hence applying 
120898 days forward to this date, we arrive at the date Dec. 20, 
648 A.D., on which the new-moon happened with which the 
lunar Agrahayana ended this year. 

Now on the day of the last quarter of this month or the 
astaka which fell on the 13th Dec., 648 A.D., the moon was 
conjoined with Citrd or a Virginis, in the latter part of the 
night. 

On this day, at G. M. N., we had 



Hence 

Apparent Sun =265 8'. 
Moon- 179 10', 
' 



Mean Sun =284 57' 0"'47, 

, , Moon = 180 14' 22" ' 10, 

Lunar Perigee =188 B2' 84"'17, 

Sun's Apogee = 79 46' 40" '79. Long, of a 7z>^mis = 185 neaily 

From these calculations ife follows that the last lunar month 
of the year, was the second Agrahayana as this month completed 
the luni-solar cycle of 331 years. 

The date of the inscription, being the second day of the 
second Igrahayana, was the 22nd of November, 648 A.D. 
With this second Agrahfnjana which ended on the 20th Dec., 



2 Length of Solar Agiahajana^ZSda. 30. 24v. 2 m 33^ ^Burgess 8. Siddlianta, 
v,8). 
Length of Lunar month =29da. 31n 50v. 6* 53rr (ace. to the Khanfakhadyaha). 



INDIAN E1UB 251 

648 A.D., the year 330 of the Gupta era ended. It must be 
admitted that the inscription as it has been read or as it was 
executed was slightly defective. In this case also Aryabhata I' 8 
Caitra-Sukladi reckoning is not followed. 

Here 330 of the Gupta era = 649 A.D. 
.'. Zero of the =310 A.D. 

V. Morvi Copper Plate Inscription 

r WTRT 



This inscription says that on the day of the 5th tithi of the 
light half of lunar Phdlguna of the Gupta year 585, the king of 
the place Morvi (22 49' N and 70 53' E) made a gift at the time 
of a solar eclipse, which happenei =?ooie time before this date, on 
which the deed of gift, viz., the copper plate in question, was 
executed. 

To find the date of this copper plate, had been a pit-fall for 
Dr, Fleet, who mistook that the solar eclipse in question 
happened on the 7th May, 905 A.D. Now the year 585 of the 
Gapta should be 904 A.D. and the date of execution of the plate 
should be Feb. 20, 904 A.D. We looked for the solar eclipse, 
two lunations + 5 days before" and 8 lunations* 5 days before this 
date. Although there happened the two solar eclipses at these 
times, they were not visible in India. 

We find, however, that here the Gupta year is reckoned not 
from the light half of Pausa, but from the light half of Caitra 
according to Aryabhata I's rule. Here the year 585 of the Gupta 
era =826 of the Caitra-Sukladi Saka era =904-905 A.D., or the 
Zero year of the Gupta era = 319-20 A.D. the date of the 
inscription corresponds to March 3, 1941 A.D., and the elapsed 
years till this clate-1036 years -12814 lunations =-378405 days. 
The date of the copper plate works out to have been Feb. 12, 905 
A.D. The eclipse referred to in the inscription happened on 

i Finally accepted by Fleet-Indian Antiquary, Nov., 1891, page 382. S. B. 
Dlkit& did actually find it. 



AXOIENT INDIAN CHRONOLOGY 

Nov. 10, 904 A.D,, 1 on which, at G.M.N. or 4-44 p.m. Morvi 
time, 

Mean Sun =234 22' 29"'34, 

Sun's Apogee = 83 9' 18* '82, 

Mean Moon =231 1' 21"'80, 

D. Node =246 7' 3F10, 

Lunar Perigee =162 10' 10" '68. 

The new-moon happened at mean noon Morvi time, the 
magnitude of the eclipse as visible at the place was about '075. 
The beginning of the eclipse took place at 11-85 a.m. Morvi time, 
the end came about 12-45 noon Morvi mean time. Duration was 
about 1 hr. 10 inin. 1 

Secondly, if we use the Khandakhadyaka constants, the 
ahargana becomes for 826 of Saka era + 8 lunations = 87528. 
Hence the mean places with Lalla's corrections thereto, at 
G-.M.N. at the same day, become : 

Mean Sun =228 18' 5", 

Moon =224 27' 86", 

D. Node =239 44' 56", 

Lunar Perigee =155 69' 47". 

It appears that this eclipse could be predicted by the method 
of the Khandakhadyaka. The gift made by this copper plate was 
probably a reward to the calculator of the eclipse. 

VI. The Sixth Instance of Gupta Inscription Date 



^n i 

In the year 156 of the Guptas, which was the Jovial year 
styled the Maha-vaU'dkha year, the inscription records the date as 
the day of the 3rd lithi of the light half of Kdrtika. 

Now 156 of the Gupta era =475 A.D. 

Julian days on Jan. 1, 475 A.D. =1894552, and 

,, ,, 1900 A.D. =2415021. 

The difference is 520469 days which comprise 14*'24 Julian 
centuries +253 days.- We incrr-ase 520469 days by 12'25 days and 

1 The above circumstances of the eclipse have been calculated by my collaborator, 
Mr. N. 0. Lahiri, M*A. 

2 Pleet Gupta Inscriptions, page 104, the Kh6h Grant. 



INDIAN ERAS 25B 

arrive at the date, Dec. 20, 474 A,D., on which, at G.M.T. 6 br*. 
or 11-4 a.m. Ujjayim M-.T., 

Mean Jupiter =170 54' 6''.57, 
Mean Sun =269 47' IF. 66. 

Henoe we calculate that mean Jupiter and mean Sun became 
nearly equal 289 days later, i.e., on the 17th September, 475 
A.D., at6a.no. G.M.T. f 

Mean Jupiter = 194 55' 34" '42, 
Mean Sun = 194 38' 19" 15. 

It is thus seen that the mean places would become almost 
equal in 6 hrs. more. For the above mean places, however, 
the equations of apsis for Jupiter and Sun were respectively 
-2 6' 4 //f 01 and -1 45 ; 2"'70. Hence their apparent places 
became as follows : 

Appt. Jupiter = 192 49' 30"'4L 
Sun = 192 53' 16" '45. 

Thus they were very nearly in conjunction at hrs. G.M.T* 
on the 17th September, 475 A.D. 

According to Brahniagupta, Jupiter rises on the east on 
getting at the anomaly of conjunction of 14. This takes place 
in 15-5 days. Hence the date for ihe heliacal rising of Jupiter 
becomes the 2nd October, 475 A.D, at G.M.T. 18 hrs. when- 

Appt. Sun =208 45', and 
Jupiter =196 20' nearly. 

Thus Jupiter was heliacally visible about Oct. 20, 475 A.D 
The actual date of the inscription was Oct 18, 478 A.D. 



the modern Surya ^anta^, i 8 475 A.D- the date of the 
on the new-moon prior to October 1, 4/0 A . 



2,34 ANCIENT INDIAN CHRONOLOGY 

inscription, which took place on Oct. 15-lfi of the year, gave 
the name of the year. The sun would reach the naksatra 
Anuradha, and the year begun was consequently M alia vaisakha 
year of Jupiter. 

This inscription also shows that the Gupta era began from 
319 A.D. 

VII. The Seventh Instance of Gupta Inscription Date 



The inscription records the date as the year 16.3 of the Gupta 
kings, the Jovial year called Maha Asvayuja, the day of the 
2nd titlii of the light half of Caitra.' 

The year 163 of the Gupta era- or 482 A,D. was similar to the 
year 1941 A.D., and the date to March 30, 1941 A-D. In 1459 
sidereal years (1941-482=1459), there are 532909 days, which 
are applied backward to the SOth March, 1941 A.D., and we 
arrive at the tentative date of the inscription as March 8, 482 
AJ). On this date, at G.M.N., we bad- 

Mean Jupiter = 29 58' 8"*24, 
Sun = 347 12'47"*11. 

Here, Jupiter's heliacal setting is yet to come in about 
30 days. Hence on April 7, 482 A.D., 

Mean Jupiter = 32 27' 46"'22, 

Sun = 16 46' 57"*02 at G.M.N. 

Thus the heliacal setting of Jupiter took place in two days 
more according to Brahrnagupta's rule on the 9th April, 482 
A.D., and the new-moon happened on the 5ih April, 482 A.D., 
when the sun was in the naksatra Bharatil. Hence the year to 
come got its name Asvayuga year. But the tentative date of 
the inscription was obtained as March 8, 482 A.D , which was 
21 days before the new-moon on about the 5th April, 482 A.D. 
This weeds elucidation. 

- i- Fleet Gupta. Inscriptions, page 110, the Kh&h Grant II 



INDIAN BRAS - 255 

Here by coming down by 30 days we arrive at the lunar 
month of Vaisaklia as it is reckoned now. But in the year 482 
A.D., i.e., 17 years before the year 499 A.D., when the Hindu 
scientific siddhantas came into being, the calendar formation 
rale was different. In our gauge year 1941 A.D. the moon of 
last quarter got conjoined with Gitrd or a Virginia, on the fc 20th 
Jan. before sunrise. Hence as pointed out before in this gauge 
year 1941 A.D. also, the lunar Agrahdyana of the early Gupta 
period ended on the 27th Jan., 1941 A.D. Thus the lunar month 
that is now called Pawja in 1941 A ,D, was called Agrahayana in 
482 A.D. Hence thv> lunar Caitra of 482 A.D. is now the 
lunar Vaisdkha of 1941 A.D. 

The date of this inscription is thus correctly obtained as the 
7th April, 482 A.D.; the Jovial year begun was a Mahd 
Isvayuja year. This instance also shows tuat the Zero year 
of the Gupta era was approximately the same as the Christian 
year 319 A.D. 

VIII. The Eighth Instance of Gupta Inscription Date 



This inscription records the date, as the year 191 of the 
Gupta emperors, the Jovial year of Mahd-caitra, the day of the 
third tithi of the dark half of lunar Magha, 

We first work out the date on the hypothesis that the Gupta 
jear was in this case also reckoned from the light Lalf of lunar 
Paiisa. The Gupta year 191, on this hypothesis, would be similar 
to the Christian year 1931, and the date of the inscription would 
correspond with March 6, 1931 A D< Now this Gupta year 
191 = 510 A.D., would be later il.an the time of Aryabhata I, 
viz., 409 A.D., by 11 jeans 

The elapsed years (sidereal) are 1421, which comprise 17576 
lunation s = 519029 days. These days are applied backward to 
the date, March 6, 1931 A.D., and we arrive at the date. Feb. 
12, 510 A.D. 

1 FJeet Guptd Inscriptions, page 114, the Majhgav&m Graufc, 



256 .ANCIENT INDIAN CHRONOLOGY 

On this date, Feb. 12, 510 A.D., at G.M.N,, we bad- 

Mean Jupiter = 158 8' 3"*87. 

Sun = 323 46'13"'72. 

* 

We find easily the sun and Jupiter had reached equality in 
mean longitude in 133 '5 days before, when, at G.M.T. far., 

.Mean Sun = 142 54' 15'/'50 
Mean Jupiter = 142 52' 48'57. 

If these were the longitudes as corrected by the equations of 
apsis, then the haliacal visibility would come according to the 
rule of Brahmagupta abouu 15" 5 days later. The mean longitudes 
15.5 days later become 

For Sun = 158 10' 54"'2L 
For Jupiter = 144 Iff 7"'2o. 

These, corrected by the equations of apsis, become^ 

For Sun = 156 3' 27*, 
For Jupiter = 140 16' 41. 

Hence the true heliacal visibility would coine in 4 days more. 
We have here (1) gone up by 183*5 days and (2) come down 
by 15'5 days. On the whole we have gone up by 168 days or 5 
lunations +21 tithis. Thus on the day of the heliacal visibility 
of Jupiter, which came in four days more, we would have to go 
up by 164 days=5 lunations +17 tithis. This interval we have fco 
apply backward to the llth tithi of Mdgha, and we arrive at the 
first day of BMdrapada. The date of the heliacal visibility would 
thus be Sep. 1, 509 A.D., and at G.M.N. the sun's true longitude 
would be 160 9' nearly, which shows that the sun would reach 
the Hastd division, On the preceding day of the new-moon, the 
sun would be in the naltsatra U. Plialguni, and the Jovial year 
begun would be styled PMlguna or the Maha-phalguna year. 
This result does not agree with the statement of the inscription. 

It now appears that after the year 499 A.D. or iryabha-ta I's 
time, the reckoning of ihe years of the Gupta era was changed 
from the light half of Pausa to the light half of Gaitra, according 
to Iryabhata I's rule : 



Kdlakriyd, 31. 



INDIAN ERAS 249 

The true KhandakhaJyka ahargana becomes = 212179 at 
Ujjayini mean midnight of rnonday, when 

Mean Sun = 10* 24 43' 44", 

Moon = 11* 24 26' 37", 

Lunar Apogee = 6* 3 20' 53", 

A. Node = 2 s 1 59' 40". 

Hence on the same date at 6 a.m., Ujjayini M.T., 

Mean Sun = 10* 23 59' 23", 

- Sun's Apogee = 2 s 17 0' 0", 

Mean Moon = 11* 14 38' 41", 

Lunar Apogee = 6* 3 15' 52" - Moon = 342 ' 56/ 51 "' 

.'. Moon -Sim = 16 57' 25" 

57' 25". 



Appl. Sun = 325 59' 2", 



On this Monday, the tithi was the second of the light half of 
unar Phalgnna, while the sun's longitude shows that the 
Bengali date was the ^4th of solar Phalguna. We are here 
in agreement with DIksita. 

In this case also calculation by the modern methods is 
unnecessary as the time was later than of Brahmagupta. It 
should be noted that the old year-reckoning from the light half 
of Pausa persists inspite of Iryabliata I's rule of reckoning it 
from the light half of Caitra. Here also 927 of the Gupta Bra 
= 1246 A.D. 

.'. Zero year of the Gupta Era = 319 A.D. 
IV. The Fourth Instance of Gupta Inscription Date 

\\* 38 *nra fgFnwft gf^ ^ t 1 

This states that the Gupta year 330 had at its end the second 
Agralidyana. Here, the Gupta year 330, up to Agrahdyana, 
the time by the Caitra-^uUddi Saka era would be 570 years + 
9 months. 

According to the Khandakhddyaka of Brahmagupta the total 
Kali-solar days up to 570 of Saka elapsed + 9 months = 
1349910, in which we get 1383^ intercalary months, i.e., 
1383 exuct intercalary months by the mean rate, which tends 
to show that there was a second lunar Agrahdyana at this time. 
But this explanation appears unsatisfactory. If we follow the 

1 FleetGupta Inscriptions, page 92,, the Kaira (2245'N, 7245'E) Grant. 
&!~ 1408B 



250 ANCIENT INDIAN CHRONOLOGY 

method of the Siddhantas. there can be no intercalary month in 
the solar month of Agrahayuna, of which the length as found by 
Warren is less than that of a lunar month. 2 We have also 
examined it carefully and found that in the present case this 
could not happen. We have then to examine it another way- 

On Dec. 20 of the year 317 AD., th^re was a new-moon 
with which the lunar Agmhayana eiidel and the sun turned 
north. The character of this lunar Agraliayana was that the 
last quarter was conjoine \ with Gitra or a Virginia. The Gupta, 
era was started one year later than this date, from the 20th 
Dec.,318A.D. The year 330 of the Gupta era was thus the 
year which ended about Dec, 20, 648 A.D, and the number of 
years elapsed was =331 = 160x2*11. 

Thus 381 years was a fairly complete lur.i-solar cycle, and 
comprised 120898 days. Again 577825 days before Jan. 1, 
1900 A.D,, was the date Dec. 20, 317 A.D. Hence applying 
120898 days forward to this date, we arrive at che date Dec, 20, 
648 A.D. y on which the new-moon happened with which the 
lunar Agraliayana ended this year. 

Now on the day of the last quarter of this month or the 
astakd which fell on the 13th Dec., 648 A.D., the moon was 
conjoined with Citra or a Virginia, in the latter part of the 
night. 

On this day, at G. M. N., we had 



Mean Sun =264 57' 0"'47, 

Moon =180 14' 22" '10, 

Lunar Perigee =188 32' 84"'17, 

Sun's Apogee = 79 46' 40"' 79. 



Hence 

Apparent Sun -265 8'. 
Mpon=179 10', 
Long, of a Virginia = 1QB* neaily 

From these calculations it follows that the last lunar month 
of the year, was the second AgroJidyana as this month completed 
the luni-solar cycle of 331 years. 

The date of the inscription, being the second day of the 
second Agrahayana, was the 22nd of November, 64S A.D. 
With this second Agrahayana which ended on the 20th Dec., 

2 Length of Solar AgiaMyana-^Qda. 30. 24v 2 ZII 33iv (Burgess #. Siddhanta, 
xiv, 8). 

Length of Lunar coontli =29da. 31?i. 50v. 6 Iir 53*v (ace. to the j 



INDIAN EitAS 5tti 

648 A.D,, the year 330 of the Gupta era ended. If must bt 
admitted that the inscription as it has been tead ot as it icas 
executed was slightly defective. In this case also Anjalhcda I\s 
Caitra-tfukladi reckoning is not followed. 

Here 330 of the Gupta era = 649 A.D. 
.-. Zero of the =319 A.D. 

V. Morvi Copper Plate Inscription 



u 



This inscription says that on the day of the 5th tithi of the 
light half of lunar PMlguna of the Gupta year 585, the king of 
the place Morvi (22 49' N and 70 s 53' E) made a gift at the time 
of a solar eclipse, which happened some time before this date, on 
which the deed of gift, viz., the copper plate m question, was 

executed. . , , 

To find the date of this copper plate, had been a pit- tall for 
Dr Fleet, who mistook that the solar eclipse in quest.on 
happened on the 7th May/905 A.D. Now the year 585 of the 
Gupta should be 904 A.D. and the date of execution a the plate 
should be Feb. 20, 904 A.D. We looked for the solar echpse, 
two lunations + 5 days before and 8 lunations+5 days before his 
date. Although there happened the two solar eclipses at the^e 
times, they were not visible in India. 

We find however, that here the Gupta year is reckoned not 



= 



did actually find it. 



252 AXOIBNT INDIAN CHRONOLOGY 

Nov. 10, 904 AJX, 1 on which, at G.M.N. or 4-44 p.m. Morvi 
time, 

Mean Sun =234 22' 29"'34, 

Sun's Apogee = 83 9' 18"'82, 

Mean Moon =231 I 1 21"'80, 

D. Node =246 7' 31"'10, 

Lunar Perigee = 162 10' 10"'68. 

The new-moon happened at mean noon Morvi time, the 
magnitude of the eclipse as visible at the place was about '075. 
The beginning of the eclipse took t place at 11-35 a.m. Morvi time, 
the end came about 12-45 noon Morvi mean time. Duration was 
about 1 hr. 10 inin. 1 

Secondly, if we use the Khandakhddyaka constants, the 
ahargana becomes for 826 of Saka era + 8 lunations=87528. 
Hence the mean places with Lalla's corrections thereto, at 
Q-.M.N. at the same day, become: 

Mean Sun =228 18' 5*, 

,, Moon =224 27' 36", 

D. Node =239 44' 56", 

Lunar Perigee =155 69' 47". 

It appears that this eclipse could be predicted by the method 
of the Khandakhddyaka. The gift made by this copper plate was 
probably a reward to the calculator of the eclipse. 

VL The Sixth Instance of Gupta Inscription Date 



In the year 156 of the Guptas, which was the Jovial year 
styled the Mahd-vaisdkha year, the inscription records the date as 
the day of the 3rd tithi of the light half of Kdrtika. 

Now 156 of the Gupta era =475 A.D. 

Julian days on Jan. 1, 475 A.D. =1894552, and 

,, 1900 AJD. =2416021. 

The difference is 520469 days which comprise 14'24 Julian 
centuries + 253 days. We increase 520469 days by 12 '25 days and 

1 The above circumstances of the eclipse have been calculated by my collaborator, 
Mr. N. C. Lahiri, M.A. 

a Fleet Gupta Inscriptions, page* 104, the Kh6h Grant. 



INDIAN ERAS 253 

arrive at the date, Dec. 20, 474 A.D., on which, at GUf.T. 6 hrs. 
or 11-4 a.m. Ujjayiiri ]VLT., 

Mean Jupiter =170 54' 6".57, 
Mean Sun =269 47' 11".66. 

Hence we calculate that mean Jupiter and mean Sun became 
nearly equal 289 days later, i.e., on the 17th September, 475 
A.D. , at 6 a.m. G.M.T., 

Mean Jupiter = 194 55' 34" '42, 
Mean Sun = 194 38' 19"'15. 

It is thus seen that the mean places would become almost 
equal in 6 hrs. more. For the above mean places, however, 
the equations of apsis for Jupiter and Sun were respectively 
-26'4"'01 and -145'2"'70. Hence their apparent places 
became as follows : 

Appt. Jupiter = 192 49' 30"*41, 
Sun '== 192 53' 16"'45. 

Thus they were very nearly in conjunction at 6 hrs. G.M.T, 
on the 17th September, 475 A.D. 

According to Brahrnagupta, Jupiter rises on the east on 
getting at the anomaly of conjunction of 14. This takes place 
in 15"5 days. Hence the date for Lhe heliacal rising of Jupiter 
becomes the 2nd October, 475 A.D., at G.M.T, 18 hrs., when 

Appfc. Sun =208 45', and 
,, Jupiter =196 20' nearly. 

Thus Jupiter was heliacally visible about Oct. 20, 475 A.D. 
The actual date of the inscription was Oct. 18, 475 A.D. 

Here on the day of the heliacal visibility, the sun 
waw in the naksatra Visakhd, but Jupiter was 3 40' behind the 
first point of the noksatra division, the Vernal Equinox of 
the year being taken as the first point of the Hindu sphere. 
According to the rule of naming Jupiter's years as given in 
the modern Surya Siddhanta, XIV, 16-17, it was sun's naksatra, 
on the new-moon prior to October 18, 475 A.D., the date of the 



254 ANCIENT INDIAN CHRONOLOGY 

inscription, which took place on OcL 15-10 of the year, gav 
the name of the year. The sun would reach the naksatra 
Anuradlid, and the year begun was consequently Mahd vaisdkha 
year of Jupiter.. 

This inscription also shows that the Gupta era began from 
319 A.D. 

VII. The Seventh Instance of Gupta Inscription Date 



The inscription records the date as the year 163 of the Gupta 
kings, the Jovial year called Mahd Afvayuja, the day of the 
2nd tithi of the light half of Caitra. 

The year 163 of the Gupta era or 482 A.D. was similar to the 
year 1941 A.D., and the date to March 30, 1941 A.D. In 1459 
sidereal years (1941 -482 = 1459), there are 532909 days, which 
are applied backward to the 30th March, 1941 A.D., and we 
arrive at the tentative date of the inscription as March 8, 482 
A.D. On this date, at G.M,N., we bad- 
Mean Jupiter = 29 58' 8* '24, 
Sun = 847 12' 47*11. 

Here, Jupiter's heliacal setting is yet to come in about 
30 days. Hence on April 7, 482 A.D., 

Mean Jupiter = 32 27' 46"*22, 

Sun = 16 46' 57"'02 at GKM.N. 

Thus the heliacal setting of Jupiter took place in two days 
more according to Brabmagupta's rule on the 9th April, 482 
A J)., and the new-moon happened on the oth April, 482 A.D,, 
when the sun was in the naksatra Bharatil. Hence the year to 
come got its name Asvayuga year. But the tentative date of 
the inscription was obtained as March 8, 482 A.D , which was 
21 days before the new-moon on about the 5th April, 482 A.D. 
This needs elucidation. 

* - Flesfc G-apta, Insor ipt-ions, page 110, the Kb6h Grant II 



INDIAN ERAS 2 :>5 

Here by coming down by 30 days we arrive at the lunar 
month of VaisaMa as it is reckoned now. But in the year 4M 
A.D., i.e., 17 years before the year 499 A.D., when the Hindu 
scientific siddhdntas came into being, the calendar formation 
rale was different. In our gauge year 1941 A.D. the moon of 
last quarter got conjoined with Citra or a Virgini*, on the >20th 
Jan. before sunrise Hence as pointed out before in this gauge 
year 1941 A.D. also, the lunar Agrahdyana of the early Gupta 
period ended on the- 27th Jan., 1941 A.D. Thus the lunar month 
that is now called Pausa in 1941 A.D. was called Acjrdhaywa in 
482 A.D. Hence the lunar Caiira of 482 A.D. i%> now the 
lunar VaiSdkha of 1941 A.D. 

The date of this inscription is thus correctly obtained as the 
7th April, 482 A.D.; the Jovial year began was a Maha 
Afoayuja year. This instance also shows tuat the Zero year 
of the Gupta era was approximately the same as the Christian 
year 319 A,D. 

VIII, The Eighth Instance of Gupta Inscription Date 



This inscription records the date, as the year 191 of the 
Gupta emperors, the Jovial year of Mahd-caitra. the ('ay of t! s o 
third tithi of the dark half of Inner Magha. 

We first work out the date on the hypothesis that the Gupta 
year was in this case also reckoned fiom the light Lulf oi lunar 
Pausa. The Gupta year 191, on this hypothesis, would be simi.ar 
to the Christian jear 1931, and the date of the inscription would 
correspond with March 6, 1931 A D. Now th;s Gupta year 
191 = 510 A.D., would be later tl an the time of Aryabhata I, 
viz., 499 A.D., by 11 jears 

The elapsed years (sidereal; are 14^1 . which comprise 17576 
lunation s= 519029 days. These days are applied backward to 
the date, March 6, 1931 A.D., and we arrive at the date. Feb. 
12, 510 A.D. 

1 FJeet Gupta Inscriptions, page 114, the Majbgavam Grant. 



256 ANCIENT INDIAN CHRONOLOGY 

On this date, Feb. 12, 510 A.D., at G.M.N., we bad- 

Mean Jupiter = 158 8' 8"'87. 
Sun = 323 46' 13"'72. 

We find easily the sun and Jupiter had reached equality in 
mean longitude in 133'5 days before, when, at G.M.T. hr., 

Mean Sun = 142 54' 15"*50 
Mean Jupiter = 142 52' 48*57. 

If these were the longitudes as corrected by the equations of 
apsis, then the hsliacal visibility would come according to the 
rale of Brahmagupta about 15*5 days later. The mean longitudes 
15.5 days later become 

~~ For Sun = 158 Iff 54"*21. 

For Jupiter = 144 Iff 7'"25. 

These, corrected by the equations of apsis, become- 

For Sun = 156 3' 27", 
For Jupiter = 140 16' 41. 

Hence the true heliacal visibility would come in 4 days more. 
We have here (1) gone up by 183*5 days and (2) come down 
by 15*5 days. On the whole we have gone up by 168 days or 5 
lunations +21 tithis. Thus on the day of the heliacal visibility 
of Jupiter, which came in four days more, we would have to go 
up by 164 days=5 lunations +17 tithis. This interval we have to 
apply backward to the llth tithi of Maglia, and we arrive at the 
first day of Bhddrapada. The dafce of the heliacal visibility would 
thus be Sep. 1, 509 A.D., and at G.M.N. the sun's true longitude 
would be 160 9' nearly, which shows that the sun would reach 
the Hastd division. On the preceding day of the new-moon, the 
sun would ba in the naksatra U. Phalguni, and the Jovial year 
begun would be styled Phdlguna or the Mahd-phdlguna year. 
This result does not agree with the statement of the inscription. 

It now appears that after the year 499 A.D. or Aryabhata Fs 
time, the reckoning of the years of the Gupta era was changed 
from the light half of Pausa to the light half of Caitra, according 
to Aryabhata I's rule : 



Kdlakriyd, 31. 



INDIAN ERAS 249 

The true Khandakhddyka ahargana becomes = 212179 at 
Ujjayini mean midnight of rnonday, when 

Mean Sun = 10* 24 43' 44", 

,, Moon = II 5 24 26' 37", 

Lunar Apogee = 6 s 3 #)' 53", 

A. Node = 2' 1 59' 40". 

Hence On the same date at 6 a.m., Ujjayini M.T., 

Mean Sun = 10* 23 59' 23", mi 

Thus 
Sun's Apogee = 2' 17- 0' (F = 3230 

Mean Moon - 11 14 33 4 , PP = , 

Lunar Apogee = 6* 3 15' 52" * 

.'. Moon -Sun = 16 57' 25" 

= 1 tft&i+4 57' 25". 

On this Monday, the Wf/ii was the second of the light half of 
unar Phalguna, while the sun's longitude shows that the 
Bengali date was the 24th of solar Phalguna. We are here 
in agreement with Dlksita. 

In this case also calculation by the modern methods is 
unnecessary as the time was later than of Brahmagupta. It 
should be noted that the old year-reckoning from the light half 
of Pansa persists inspite of iryabhata I's rule of reckoning it 
from the light half of Caitra. Here aleo 927 of the Gupta Era 
= 1246 A.D. 

/. Zero year of the Gupta Era = 319 A.D. 

IV. The Fourth Instance of Gupta Inscription Date 



39 

This states that the Gupta year 330 had at its end the second 
Agrahayana. Here, the Gupta year 330, up to Agrahayana, 
the time by the Gaitra-iSukladi Saka era would be 570 years + 
9 months. 

According to the Khandakhadyaka of Brahmagupta the total 
Kali-solar days up to 570 of Saka elapsed + 9 months = 
1349910, in which we get 1383-^ intercalary months, i.e., 
1383 ex ict intercalary months by the mean rate, which tends 
to show that there was a second lunar Agrahayana at this time. 
But this explanation appears unsatisfactory. If we follow the 

1 Fleet Gupta Inscriptions, page 92,, the Kaira (2245'N, 7245'E) Grant. 
8-2 1408B 



250 ANCIENT INDIAN CHRONOLOGY 

method of the Siddhantas . there can be no intercalary month in 
the solar month of Agrahayana, of which the length as found by 
Warren is leas than that of a lunax month. 2 We have also 
examined it carefully and found that in the present case this 
could not happen. We have then to examine it another way, 

On Dec. 20 of the year 317 AD., th*-re was a -new-moon 
with which the lunar Agralwyana eiidel and the sun turned 
north. The character of this lunar Agrahayana was that the 
last quarter was conjoine ] with Cltrd or a Virginis. The Gupta 
era was started one year later than this date, from the 20th 
Dec.,318A.D. The j ear 330 of the Gupta era was thus the 
year which ended about Dec. 20, 618 A,D, and the number of 
years elapsed was =331 = 160x2 + 11. 

Thus 331 years was a fairly complete lur.i-solar cycle, and 
comprised 120898 days. Again 577825 days before Jan. 1, 
1900 A.D., was the date Dec. 20, 317 A,D, Hence applying 
120898 days forward to this date, we arrive at the date Dec. 20, 
648 A.D., on which the new-moon happened with which the 
lunar Agrahayana ended this year, 

Now on the day of the last quarter of this month or the 
astaka which fell on the 13th Dec., 648 A.D., the moon was 
conjoined with Citrd or a Virginis, in the latter part of the 
night. 

On this day, at G. M. N., we had 



Hence 

Apparent Sun =265 8'. 
Moon =179 10', 



Mean Sun =264 57' 0"*47, 

,, Moon =180 14' 22"'10, 

Luaar Perigee =188 82' 84"'17, 

Sun's Apogee = 79 46'" 40"*79. Long, of a 7z>0zm's = 185 neaily 

From these calculations ifc follows that the last lunar month 
of the year, was the second Agrahdyana as this month completed 
the luni-solar cycle of 331 years. 

The date of the inscription, being the second day of the 
second Igrahayana, was the 22nd of November, 643 A.D. 
With this second Agnthdyana which ended on the 20th Dec., 



2 Length of Solar AgiaMjana = %$da. 30n. 24v, 2 1 " 33 IV (Burgess 8. SiddMnta, 
xiv,8). 

Length of Lunar month =29da. Sin, 50v.'6* 53 (ace. to the 



INDIAN EHAS 

648 A. D., the year 330 of the Gupta era ended. 11 must 
admitted that the inscription as it has been read or a* it 
executed was slightly defective. In this cane also Arijabltatti 1's 
Caitra-SiMndi reckoning is not followed. 

Here 330 of the Gupta, era = 649 A.D. 
.-. Zero of the =320 A.D. 

V. Morm Copper Plate Inscription 



wii 



'TOT 



This inscription says that on the day of the 5th tithi of the 
light half of lunar Phalguna of the Gupta year 583, the king of 
the place Morvi (22 49' N and 70 53' E> made a gift at the tirae 
of a solar eclipse, which happened rame time before this date, on 
which the deed of gift, viz., the copper plate in question, was 

executed. 

To find the date of this copper plate, had been a pit-fall for 
Dr. Fleet, who mistook that the solar eclipse in question 
happened on the 7th May, 905 A.D. Now the year 535 of the 
Gupta should be 904 A.D. and the date of execution . the plate 
should be Feb. 20, 904 A.D. We looked for the solar eclipse, 
two lunations + 5 days before and 8 lunations + 5 days before this 
date. Although there happened the two solar eclipses at these 
times, they were not visible in India. 

We find, however, that here the Gupta year is reckoned not 
from the light half of P*, but from the light half o i Crt 
according to Aryabhata I's rule. Here the year 080 of the Gupta 

r=826of Jcaitr^umdi aka era=904-905 A^D or he 
Zero year of the ^ - ^ < u d 



p in al ly accepte 
&d actually find it. 



252 ANCIENT INDIAN CHRONOLOGY 

Nov. 10, 904 AJX, 1 on which, at G.M.N. or 4-44 p.m. Morvi 

time, 

Mean Sun =234 22' 29"'34, 
Sun's Apogee = 83 9' 18'/'32, 
Mean Moon =231 7' 21"*80, 
D. Node =246 7'31"'10, 

Lunar Perigee = 162 10' 10"*68. 

The new-moon happened at mean noon Morvi time, the 
magnitude of the eclipse as visible at the place was about '075. 
The beginning of the eclipse took place at 11-35 a.m. Morvi time, 
the end came about 12-45 noon Morvi mean time. Duration was 
about 1 hr. 10 min. 1 

Secondly, if we use the Khandakhadyaka constants, the 
ahargana becomes for 826 of Saka era + 8 lunations-87528. 
Hence the mean places with Lalla's corrections thereto, at 
G.M.N. at the same day, become: 

Mean Sun =228 18' 5", 

Moon =224 27' 36", 

D. Node =289 44' 56", 

Lunar Perigee =155 69' 47". 

It appears that this eclipse could be predicted by the method 
of the Khandakliadyaka,. The gift made by this copper flate was 
probably a reward to the calculator of the eclipse. 

VI. The Sixth Instance of Gupta Inscription Date 



In the year 156 of the Guptas, which was the Jovial year 
styled the Maha-vaisaklia year, the inscription records the date as 
the day of the 3rd tithi of the light hgilf of Kdrtika. 

Now 156 of the Gupta era =475 A.D. 

Julian days on Jan. 1, 475 A.D. =1894552, and 
1900 A.IX =2416021. 

The difference is 520469 days which comprise 14*24 Julian 
centuries + 253 days. We increase 520469 days by 12*25 days and 

1 The above circumstances of the eclipse have beeu calculated by my collaborator, 
Mr. N. C. Lahiri, M.A. 

* Fleet Gupta Inscriptions, page 104, the Kh6h Grant. 



INDIAN BE AS 253 

arrive at the date, Dec. 20, 474 A,D., on which, at G.M.T.6 hrs. 
or 11-4 a.m. Ujjayini M>T., 

Mean Jupiter =170 54' 6".57, 
Mean Sun =269 47' IV M. 

Hence we calculate that mean Jupiter and mean Sun became 
nearly equal 289 days later, i.e., on the 17th September, 475 
A.D., at 6 a.m. G.M.T., 

Mean Jupiter = 194 55' 34"'42, 
Mean Sun = 194 38' 19"'15. 

It is thus seen that, the mean places would become almost 
equal in 6 hrs. more. For the above mean places, however, 
the equations of apsis for Jupiter and Sun were respectively 
-26'4"'01 and -1 45' 2 //4 70. Hence their apparent places 
became as follows : 

Appt. Jupiter = 192 49' 30"'41, 
Sun = 192 53' 16"''45. 

Thus they were very nearly in conjunction at 6 hrs. GKM.T, 
on the 17th September, 475 A.D. 

According to Brahmagupta, Jupiter rises on the east on 
getting at the anomaly of conjunction of 14. This takes place 
in 15'5 days. Hence the date for the heliacal rising of Jupiter 
becomes the 2nd October, 475 A.D,, at G-.M.T. 18 hrs., when 

Appt. Sun =208 45', and 
,, Jupiter =196 20' nearly. 

Thus Jupiter was heliacally visible about Oct. 20, 475 A.D. 
The actual date of the inscription was Oct. 18, 475 A.D. 

Here on the day of the heliacal visibility, the sun 
was in the naksatra Viakha, but Jupiter was 3 40' behind the 
first point of the naksatra division, the Vernal Equinox of 
the year being taken as the first point of the Hindu sphere. 
According to the rule of naming Jupiter's years as given in 
the modern Surya Siddhanta, XIV, 16-17, it was sun's naksatra, 
on the new -moon prior to October 18, 475 A.D.. the date of the 



254 ANCIENT INDIAN CHRONOLOGY 

inscription, which took place on Oct. 15-lfi of the year, gave 
the name of the year. The sun would reach the naksatra 
Anuradha, and the year begun was consequently Mahd vai&aklia, 
year of Jupiter. 

This inscription also shows that the Gupta era began from 
319 A.D. 

VII. The Seventh Instance of Gupta Inscription Date 



The inscription records the date as the year 163 of the Gupta 
kings, the Jovial year called Maha Asvayuja, the day of the 
2nd tithi of the light half of Caitra. 

The year 163 of the Gupta era or 482 A.D. was similar to the 
year 1941 A.D., and the date to March 30, 1941 A.D. In 1459 
sidereal years (1941-482 = 1459), there are 532909 days, which 
are applied backward to the 30th March, 1941 A. D., and we 
arrive at the tentative date of the inscription as March 8, 482 
A.D, On this date, at G.M.N., we had 

Mean Jupiter = 29 58' 8" '24, 
Sun = 347 12' 47" '11. 

Here, Jupiter's heliacal setting is yet to. come in about 
30 days. Hence on April 7, 482 A.D., 

Mean Jupiter = 32 27' 4V' 22, 

Sun = 16 46' 57" -02 at GKM.N. 

Thus the heliacal setting of Jupiter took place in two days 
more according to Brahxnagupta's 1 rule on the 9th April, 482 
A .D., and the new-moon happened on the oth April, 482 A.D,, 
when the sun was in the naksatra BharanL Hence the year to 
come got- its name Afoayuga year. But the tentative date of 
the inscription was obtained as March 8, 48*2 A.D , which was 
21 days before the new-moon on about tiie 5th April, 482 A.D. 
This needs elucidation. 

l Fleet Gupta Inscriptions* page 110, the Kbdh Grant II 



INDIAN BE AS 255 

Here by coming down by 30 days we arrive at the lunar 
month of Vaifdkha as it is reckoned now. But in the year 482 
A.D., i.e., 17 years before the year 499 A.D.., when the Hindu 
scientific siddhdntas came into being, the calendar formation 
rale was different. In our gauge year 1941 A.D. the moon of 
last quarter got conjoined with Gitra or a Virginis, on the 20th 
Jan. before sunrise. Hence as pointed out before in this gauge 
year 1941 A.D. also, the lunar Agrahdyana of the early Gupta 
period ended on the 27th Jan., 1941 A.D. Thus the lunar month 
that is now called Pausa in 1941 A,D. was called Agrahdyana in 
482 A.D. Hence the lunar Caitra of 482 A.D. is now the 
lunar Vaisdkha of 1941 A.D. 

The date of this inscription is thus correctly obtained as the 
7th April, 482 A.D.; the Jovial year begun was a Maha 
Asvayuja year. This instance also shows taafc the Zero year 
of the Gupta era was approximately the same as the Christian 
year 319 A.D. 

VIII. TJie Eighth Instance of Gupta Inscription Date 



This inscription records the date, as the year 191 of the 
Gupta emperors, the Jovial year of Mahd-caitra, the c?ay of the 
third tithi of the dark half of lunar Magha. 

We first work out the date on the hypothesis that the Gupta 
year was in this case also reckoned from the light half of lunar 
Pausa. The Gupta year 191, on this hypothesis, would be similar 
to the Christian jear 3931, and the date of the inscription would 
correspond with March 13, 1931 A D. Now this Gupta year 
191=510 A.D., would be later clan the time of Aryabhata I, 
viz., 499 A.D., by 11 3 ears 

The elapsed years (sidereal) are 1431, which comprise 17576 
lunation s= 519029 dnys. These days are applied backward to 
the date, March 6, 1931 A.D., and we arrive at the date, Feb. 
12, 510 A.D. 

1 FJeet Gupta Inscriptions, page 114, the Majhgavam Grant. 



2 t 56 ANCIENT INDIAN CHRONOLOGY 

On this dale, Feb. 12, 510 A.D., at G.M.N., we bad- 

Mean Jupiter = 158 8' 3"*87. 
Sun = 323 46' 13"'72. 

We find easily the sun and Jupiter had reached equality in 
mean longitude in 133'5 days before, when, at G.M.T. hr., 

Mean Sun = 142 54? 15"'50 
Mean Jupiter = 142 52' 48'57. 

If these were the longitudes as corrected by the equations of 
apsis, then the heliacal visibility would coine according to the 
rule of Brahmagupta about 15*5 days later. The mean longitudes 
15.5 days later become 

For Sun = 158 10' 54^21. 
For Jupiter = 144 10' 7"*25. 

These, corrected by the equations of apsis, become 

For Sun 156 3' 27*. 
For Jupiter = 140 16' 41. 

Hence the true heliacal visibility would come in 4 days more. 
We have here (1) gone up by 183'5 days and (2) couae down 
by 15*5 days. On the whole we have gone up by 168 days or 5, 
lunations +21 tithis. Thus on the day of toe heliacal visibility 
of Jupiter, which came in four days more, we would have to go 
up by 164 days=5 lunations +17ttt7w>. This interval we have to 
apply backward to the llth tithi of Magha, and we arrive at the 
first; day of Bhadrapada. The date of the heliacal visibility would 
thus be Sep. 1, 509 A.D., and at G.M.N. the sun's true longitude 
would be 160 9' nearly, which shows that the sun would reach 
the Hastd division. On the preceding day of the new-moon, the 
sun would be in the naksatra U. Phalgunl, and the Jovial year 
begun would be styled Phalguna or the Maha-phdlguna year. 
This result does not agree with the statement of the inscription. 

It now appears that after the year 499 A.D. or Aryabhata Fs 
time, the reckoning of the years of the Gupta era was changed 
from the light half of Pausa to the light half of Caitra, according 
to Aryabhata Ts rule : 



Kdlakriya, II. 



INDIAN ERAS 241 



On June 16, 63 B.C., at G. M. N., we bad- 



Mean Sun = 81 38' 59"'72, 

Moon = 80 20' 8"'16, 

Lunar Perigee = 76 0' 2" '58, 
Sun's Apogee = 67 39', 

Mean Jupiter = 80 52' 26" '87, 

Jupiter's Perihelion =341 34' 32", 
Eccentricity = '0443845. 



Hence 
Appt. 



., Sun =81 11' 
Jupiter as corrected by the 

equation of apsis, 

= 85 54' 54". 
v Cancn =97 5'. 



Jupiter had set already and the rew-moon happened in the 
naksatra Punarvasu ; the Jovial year begun was thus Pausa or 
MaMpausa. The longitude of the oldest first point of the Hindu 
sphere was about, -6 in this year and consequently the longitude 
of the first point of the Pusyd division ^as=87"20'. Jupiter \\as 
very near to this point. It may thus be inferred that the signal 
from Jupiter's position as to the beginning of the Krtayuga 
was taken to occur on this date, viz., June 16, 63 B.C. 

Again on July 16, 63 B.C., at Gr.M.T. Ohr.,or exactly one 
synodic month later 



Mean Sun =110 43' 37"'39, 

n Moon =109* 2'21"'48, 

Lunar Perigee 79 17' 18* '71, 

Mean Jupiter - 83 19' 35" '21. 



Hence - 

Appt. Moon = 110 67', 

Sun =109 23>, 
Jupiter as corrected by the 

eqn. of apsis = 88 19'. 



On this day also the sun, moon, Jupiter and the naksatra 
Pusyd were in the same cluster. This day also most probably 
afforded another signal for the coming of the Krtayuga. Jupiter 
had become heliacally visible about 10 days before. 

If we go forward by 12 lunations from the above date, we 
arrive at July 5, 62 B.C., on which, at G.M.N., 



Mean Sun =100 8' 20" '52, 
Moon =1004'19"'20, 
Jupiter = 112 47' 44"'98. 
S Cancri =100 4' nearly. 



Here was another combination of the planets, which might 
have persuaded men that the Kflayuga had begun 

On the whole it is thus established that both he lun, 
Bolar and the luni-solar-Jovial-stelkr combined ^8^ * the 
TegLing of the Krtayuga, could be observed and e.t.maed 
be g innin ^ san , s reaohing the 

in the year 63 B.C. In tniB y 
winter solstice happened on Dec. M, 



242 ANCIENT INDIAN CHBONOLOQY 

day of Pausa was the day following it. The actual starting 
of the Krta, Malava or the Samvat era was made 5 years later 
from the full-moon day of about the 28th Dec., 58 B.C. 
The Samvat year 1 was thus almost the same as 57 B.C., 
and that the number of the Samvat era represents the current 
year as in the Christian era. Further the lunar months here are 
full-moon ending as originally in the Safca era, as we have seen in 
the preceding chapters. The year was reckoned from the full- 
moon day of Paiisa. In 499 A.D. or some years later than this 
date, the Gaitra-Sukladi reckoning was followed according to the 
rule of Iryabhata. But in the Samvat era, we are told that the 
lunar months are still reckoned as full-moon ending, which is 
now a case of a queer combination of opposites. We next turn 
to solve the last problem from the epigraphic source in relation 
to this era, 

Mahva Samvat 529 , the Second Day of the Light Half of 
Phalguna and the Beginning of Spring 

In Fleet's Gupta Inscriptions, Plate No. 18, it is stated that 
spring had set in on the second day of the light half of Phalguna 
of the Malava Samvat 529 or 473 A.D. Now the year in our 
time which was similar to 529 of the Malava era was 1932 A.D., 
and the date, to March 9, 1932. Elapsed years till this date 
was-1459 sidereal years* 18046 luoations- 5320909 days. These 
days are applied backward to March 9, 1932 A.D., and we arrive 
at the date : 

Feb. 15, 473 A.D., on which, at the DjjayinI mean mid- 
night, 



Hence 

Appt. Sun =328 48' 24", 



Moon =360 20' 



Mean Sun, =326 58' 8" '09 1 

,. Moon =3550 S7/22//-72, 

Lunar Perigee =233 43' 28"*68, 
Sun's Apogee = 75 4$ 140-81' 

,, Eccentricity ='017323, 

^830 9 ^ D BPriDg be8i ' 18 ' Wll6n lhe S ' S lon itude 



nearly. 



8 .. ) 

473 A.D. The local editions probably brought fo 
spring earlier. J M 



INDIAN ERAS 248 

Again 2*5 days before Feb. 15, 473 A.D., at Ujjayini mean 
midnight, or on the 13th February, 473 A.D.. at Ujjayini mean 
midday : 

Mean Sun =324 30' 47'/'25, 

Mean Moon =328 0' 55"'12, 
Lunar Perigee = 233 26' 46" '04; 

It appears that the new-moon had happened about 3J hrs. 
before, and the first visibility of the crescent took place on the 
evening of the next day, the 14-th Feb. Thus Feb. 15 was the 
second day of the month, as stated in the inscription. 

We now proceed to consider why there has been an error in 
estimating the beginning of spring, which according to an old 
rule should come 60 days after the winter solstice day. We find 
that 60 days before this date, viz., Feb. 15, or, on : 

Dec. 17, 472 A. D., at Ujjayini mean midday, 

Mean Sun =267 20' 87*, 

Moon =284 48' 4", 

- Lunar Perigee=226 59' 5". 

The estimated winter solstice day was thus premature by about 
two days. On this day, the first visibility of the crescent took 
place in the evening. Hence the second day of the light half of 
Phdlguna was the estimated beginning of spring, i.e., 60 days 
later. The new-moon happened on the 16th December and 
the real winter solstice day was the 19th December. 

This inscription shows that the Gupta era cannot be identi- 
fied with the Savhvat era. The point that why or how the 
Malava era came to be called Vikrama Suhvat cannot be 
answered from any astronomical data, 

Note. We have here tried to interpret the astronomical 
statement of the Mandasor stone inscription of Kumara Gupta 
and Bandhuvarman. The date of the inscription found here as 
Feb 15 473 A.D., was that of the thorough repair and decora- 
turn of ie sun temple at Mandasor (>24'3'N and 75*S'E). The 
inscription says that spring lists set in. 



CHAPTER XXY 

INDIAN EEAS 
The Gupta Era 

In the present chapter, it is proposed to determine the 
beginning of the era of the Gupta emperors of northern India. 
Dr. Fleet in his great book Inscriptionum I ndi car am. Vol. Ill, has 
published a collection of the Gupta inscriptions. In order to 
verify the dales in those inscriptions he had the assistance of the 
late Mr. S. B. Diksita of Poona, and his calculations led Dr. 
Fleet to conclude that the Gupta era began from 319-21 A.D. 1 
This indefinite statement or inference is not satisfactory. Mr. 
Diksita was also not able to prove that the Gupta and Valabhi 
eras were but one and the same era. 2 Of recent years some have 
even ventured to prove that the Gupta era is to be identified with 
the Samvat or Malava era. Hence it has become necessary to 
try to arrive at a definite conclusion on this point, viz., the true 
beginning of the Gupta era. 

The tradition about this era is recorded by Alberuni, which is 
equivalent to this : From the Saka year, deduct 241, the result is 
the year of the Gupta kings and that the Gupta and Valabhi 
eras are one and the same era. 8 Now the Saka era and the 
Samvat or Malava era are generally taken to begin from the light 
half of lunar Caitra. As has been stated already, it, is extremely 
controversial to assume if this was so at the times when these 
eras were started. 

From the earliest Vedic times and also from the Veddnga 
period, we have the most unmistakable evidences to show that 
the calendar year, as distinguished from the sacrificial year, was 

i Fleet Corpus Inscriptionum Indica-raw, Vol. Ill (Gupta Inscriptions), page 127. 
3 S. B. Diksita, *TTC^te 5^tfif;*TO t page 375 (Isl Edn,). 

3 Sachau's Alberuni, Vol. II, page 7*' The epoch of the era of the Guptas 
{alls, like that of the Valabha era, 241 years later than the SakaMla." 



INDIAN EEAS 245 

started either from the winter solstice day or from the day 
following it. The so-called Caiira-8iikladi reckoning started the 
year from the vernal equinox day or from the day following it . 
So far as we can see from a study of the history of Indian 
astronomy, we are led to conclude thai this sort of beginning the 
year was started by Aryabhata I from 499 A.D. The great fame 
of Aryabhata I, as an astronomer, led all the astronomers and 
public men of later times to follow him in this respect. We 
start with the hypothesis that the Gupta era was originally 
started from the winter solstice day and that initially the year of 
the era more correctly corresponded with the Christian year, 
than with the Caitra Suklddi Saka year. 

Now the year 241 of the Saka era is equivalent to 319-20 A.D. 
We assume that the Gupta era started from the winter solstice 
day preceding Jan. 1, 319 A.D. The elapsed years of the Gupta 
era till 1940 A.D., becomes 1621 years and 1621=160x104-194-2. 
Hence the starting year of the era was similar to 1938 A.D. 
Now the mean precession rate from 319 to 1938 AJX=50'0847 
per year. Hence the total shifting of the solstices becomes till 
1938 A.D. =22 31' 27 /; '54. Thus what was 270 of the longitude 
of the "sun, should now become 291 31' nearly-a longitude 
which the sun now has about the 13th of January. On looking 
up some of the recent calendars we find that : 

(a) In the year 1922, there was a full-moon on Jan. 13. 
(t>) , 1937, ,, ,? a new-moon on Jan. 12. 

We apply ^ ela P* ed W* 1G19 < sidereal) backwald to 
Jan 12, 1937 A.D., and arrive at the date : 

Dec. 20,317 A.D., on which, at G.M.N., or Ujjayim M.T. 

5-4 p.m., 

Hence 20 =119'*5016, 

f-e 2 =1'2981, 

-H9 50 / 37 // '25, Appt. Sun =26937'. 
""257 44' 29"88, ,, Moon=2G852' nearly. 






The moon overwok to sun in about U tars and the snn 
reaped the to*r solstice in .lout 9 ho. Hence Dec 20, 
317 A D wa a new-moon da, and ate the da, of wrnter sol,t, C e 



246 ANCIENT INDIAN CHRONOLOGY 

according to the ordinary mode of Indian reckoning. As this 
day was similar to Jan. 12, 1937 A.D., viz., lunar Agrahdyana 
ended, it appears thai the Gupta era was started from about tlie 
21st Dec., 318 A.D., and this was the 12th day of lunar Pausa. 
It must be remembered in this connection, that the distinguishing 
character of the lunar Agrahdyana, with which the year ended at 
the end of a correct luni-solar cycle, was that the last quarter of 
the moon was very nearly conjoined with Citrd (Spica or 
a Virginis). 1 In our opinion this character of the month was used 
for the intercalation of a lunar month at the end of a correct 
luni-solar cycle. We now proceed to examine the dates given in 
the Gupta Inscriptions as collected together by Dr. Fleet in his 
great book on the subject. 

I. The First Instance of Gupta Inscription Date 



The inscription says that the 12th tithi of the light half of 
lunar Isddha of the Gupta year 165 fell on a Thursday. We 
examine this by both the modern and the Siddhdntic methods. 
(A) By the Modern Method, 

The year 165 of the Gupta kings is similar to the year 1924 
A.D. The elapsed years till this date = 1440 sidereal years= 
525969 days. We increase the number of days by 1 and divide it 
by 7 ; the remainder is 4, which shows that the inscription state- 
ment of Thursday agrees with the Sunday of July 13, 1924 A.D. 
We next apply 525969 days backward to July 13, 1924, and 
.arrive at the date June 21, 484 A.D., the date of the inscription. 
This date was 14'15 Julian centuries + 181'25 days before 
Jan. 1, 1900 A.D. Hence 

On June 21, 484 A.D., at G.M.N., 

Mean Sun = 91 12' 50"'64, Hence- 

Moon =235 V 53^42, 

Lunar Perigee =835 28' 2-80, 
A. Node =277 14' 51>/'51, 

Sun's Apogee = 76 14' 32", 
, , Eccentricity = '0173175. 

i Cj. the longitude of the moon on Jan. 4, 1937 A.D., at L. Q. with that of 
ints* 
Fleet's Gupta Inscriptions, page 80, Eran Inscription. 



INDIAN EEAS 247 

From these we readily find the same mean places at the 
preceding Ujjayim mean midnight. Hence 

On June 20, 484 A.D., at Ujjayini mean midnight, 
Mean Sun = 90 30' 47" '38, 



,. Moon = 225 45' 41" '78, 

Lunar Perigee =335 18' 17*61, 
A. Node =277 17' 7* '08. 



Appt. Sun = 90 2', 

M Moon =219 47' nearly. 



Thus at the Ujjayini mean midnight of the day before 
(Wednesday), the llth tithi was current, and next day, Thursday, 
had at sun rise the 12th tithi of the lunar month of Ssadlia. 

(B) According to the method of the Khandakhddyaka of 
Brahmagupta, the Kali ahargana on this Wednesday at the 
Ujjayini mean midnight was =1309545. Hence 

Mean Sun = 91 3' 4" A 

Moon =226 23' 17^ 

Lunar Perigee =335 42' 56" y 

A. Node =277 35' 17".' 

The above two sets of the mean elements for the same instant 
are in fair agreement. Hence the date of the inscription is 
Thursday, June 21, 484 4.ZX, and the Zero year of the Gupta 
era is thus 319 A,D. We are here in agreement with D'iksiia's 
finding. 

II. The Second Instance of Gupta Inscription Date 



Here the Hijrl year 662 shows the Vikrama Samvat is 
expressed in elapsed years as 1320 ; and as it is now reckoned 
it should be 1321. The Valabhi Samvat 945 is the same as the 
Gupta Samval 945, in which the 13th tithi of the dark half of 
Jyaistha fell on a Sunday. 

Now the mean Khandaklmdyaka ahargana 

= 218878 

from which we deduct 30 

211848, 
which we accept as the correct ahargana and is exactly divisible 

* Fleet Gupta Inscriptions, page 84, Veraval Inscription. 



248 ANCIENT INDIAN CHBONOLOGY 

by 7, and which was true for Saturday of Asddha vadi 12 of the 
Gupta era 945. The English date for this Saturday was May 25, 
1264 AJD, On the next day, Sunday, the date was, May 26, 
1264 A.D., the date of the inscription. 

From the above apparent ahargana for May, 25, 1264 A.D., 
which was a Saturday, at the Ujjayini mean midnight, we have 

Mean Sun = P 27 42' 48*, 
Moon = 0* 27 31' 40", 

Lunar Apogee = 6* 20 29' F (with Lalla's correction) 
A. Node = 9' 29 53' 4* ( Do. Do. Do ) 
Hence, Appt. Sun = 1* 28 21' 57", 
Moon = 0* 28 8' 44", 

Moon - Sun = 10*29 46' 47" 

= 27 tithis + 5 46' 47". 

Thus at the midnight (U.M.T.) of the Saturday ended, 
about 11 hrs. of the 13th tithi of tip-dark half of Jyaistha were 
over and 13 hrs. nearly of it remained. Thus the current tithi 
of the next morning of Sunday was also the 13th of the dark 
half of Jyaistha which is called Asddha vadi 13. 

In the present case the Valabhi or Gupta year 945 = 1264 
A.D. Hence also the Gupta era began from 319 A.D,, and we 
are in agreement with DIksita. 

III. The Third Instance of Gupta Inscription Date 



It is here stated that in the Gupta or Valabhi year 927, 
the 2nd ttthi of the light half of Phdlguna fell on a Monday! 
The English date becomes 1246 A.D., Feb. 19, Saka year 
was 1167 years + 11 months + 2 tithis, the Gupta year being 
taken to have been reckoned from the light half of lunar Pausa. 

i Fleet's Gupta Inscriptions, page 90, Veraval Inscription. 



INDIAN ERAS 249 

The true KhandakhaJ yka ahaigam becomes = 212179 at 
Ujjayim mean midnight of monday, when 

Mean Sun = 10* 24 43' 44", 

,, Moon = 11< 24 26' 37", 

Lunar Apogee = 6*3 '20' 53", 

A. Node = 2* 1 59' 40". 

Hence on the same date at 6 a.m., Ujjayini M.T., 

Mean Sun = 10* 28 59' 23", 



Sun's Apogee = 2M7 0' 0", 
Mean Moon = 11* 14 33' 4V, 
Lunar Apogee^ 6* 3 15' 52" 

.*. Moon -Sun = 16 57' 25" 

= ltitfci + 4 57' 25". 



AppL Sm " ^ 59 ' 2 "' 
- Moon = 342 S6/ 51". 



On this Monday, the tit hi was the second of the light half of 
ifnar Phalguna, while the sun's longitude shows that the 
Bengali date was the ^4th of solar Phalguna. We are here 
in agreement with Dlksita. 

In this case also calculation by the modern methods is 
unnecessary as the time was later than of Brahrnagupta. It 
should be noted that the old year-reckoning from the light half 
of P&usa persists inspite of Iryabhata I's rule of reckoning it 
from the light half of Oaitra. Here also 927 of the Gupta Bra 
= 1246 A;D. 

.'. Zero year of the Gupta Era = 319 A.D. 
IF. The Fourth Instance of Gupta Inscription Date 



This states that the Gupta year 330 had at its end the second 
Agrahdyana. Here, the Gupta year 330, up to Agrahayana, 
the time by the Gait-ra^ukladi Saka era would be 570 years + 
9 months. 

According to the Khandakhadyaka of Brahmagupta the total 
Kali-solar days up to 570 of Saka elapsed + 9 months = 
1349010, in which we get 1383^ intercalary months, i.e., 
1383 exact intercalary months by the mean rate, wlrch tends 
to show that there was a sejond luaar Agrahdyana at this time. 
But this explanation appears unsatisfactory. If we follow the 

1 Fleet-Gupta Inscriptions, page 92, the Kaira (M'45'N, 73'45'Bj Grant. 



250 ANCIENT INDIAN CHEONOLOGY 

method of the SiddMntas, there can be no intercalary month in 
the solar month of Agrahayana, of which the length as found by 
Warren is less than that of a lunar month. 2 We have also 
examined it carefully and found that in the present case this 
could not happen. We have then to examine it another way. 

On Dec. 20 of the year 317 A,D., there was a new-moon 
with which the lunar Agrahayana ended and the sun turned 
north. The character of this lunar Agrahayana was that the 
last quarter was conjoined with Citra or a Virginis, The Gupta 
era was started one year later than this date, from the 20th 
Dec., 318 A. D. The year 330 of the G-upta era ^as thus the 
year which ended about Dec. 20, 648 A.D. and the number of 
years elapsed was =331=160x2 + 11. 

Thus 331 years was a fairly complete lur.i-solar cycle, and 
comprised 120898 days. Again 577825 days before Jan. 1, 
1900 A.D., was the date Dec. 20, 317 A.D. Hence applying 
120898 days forward to this date, we arrive at the date Dec. 20, 
648 A.D., on which the new-moon happened with which the 
lunar Agrahayana ended this year. 

Now on the day of the last quarter of this month or the 
astaka which fell on the 13th Dec., 648 A.D., the moon was 
conjoined with Citra or a Virginis, in the latter part of the 
night. 

On this day, at'G. M. N., we had 



Hence 

Apparent Sun =265 Qf. 
Moon = 179 10', 



Mean Sun =264 57' 0"'47, 

Moon =180 14' 22" '10, 

Lunar Perigee =188 32' 34"17, 

Sun's Apogee = 79 46' 40"'79. Long, of a VirginiB = l8S neaily 
26118''7 I fe 2 =l''398. 

From these calculations it follows that the last lunar month 
of the year, was the second Agrahayana as this month completed 
the luni-solar cycle of 331 years. 

The date of the inscription, being the second day of the 
second Agrahayana, was the 22nd of November, 64$ A.D. 
With this second Agrahayana which ended on the 0th Dec., 



2 Length of Solar Agidliayana = %$da. 30/i. 24v. 2 ni 33 IV (Burgess S. Siddhanto 
xiv, 3). 

Length of Lunar month =29<to. 31n. 50v. 6 53iv ( acc . to the J 



INDIAN EEAS 251 

648 A.D., the year 330 of the Gupta era ended. It must be 
admitted that the inscription- as it has been read or as it was 
executed was slightly defective. In this case also Sryabhata I's 
Gaitra-3ukladi reckoning is not followed. 

Here 330 of the Gupta era- 649 A.D. 
/. Zero of the ,, =319 A,D. 

V. Morvi Copper Plate Inscription 



^ (I 
f[ H \ 

This inscription says that oa the day of the 5ih tithi of the 
light half of lunar Phdlguna of the G-upta year 585, the king of 
the place Morvi (22 49' N and 70 53' B) made a gift at the time 
of a solar eclipse, which happened some time before this date, on 
which the deed of gift, viz., the copper plate in question, was 
executed. 

To find the date of this copper plate, had been a pit-fall for 
Dr. Fleet, who mistook that the solar eclipse in question 
happened on the 7th May, 905 A.D. Now the year 585 of the 
Gupta should be 904 A.D. and the date of execution of the plate 
should be Feb. 20, 904 A.D. We looked for the solar eclipse, 
two lunations + 5 days before and 8 lunations + 5 days before this 
date. Although there happened the two solar eclipses at these 
times, they were not visible in India. 

We find, however, that here the G-upta year is reckoned not 
from the light half of Pausa, but from the light half of Gaitra, 
according to Sryabhata I's rule. Here the year 585 of the Gupta 
era =826 of the Caitra-Suklddi Saka era=904-905 A.D., or the 
Zero year of the Gupta era= 319-20 A.D. the date of the 
inscription corresponds to March 3, 1941 A. D., and the elapsed 
years till this date=1036 years = 12814 lunations =378405 days. 
The date of the copper plate works out to have been Feb. 12, 905 
A.D. The eclipse referred to in the inscription happened on 

1 Finally accepted by Fleet Indian Antiquary, Nov., 1891, page 382. S. B. 
Dlk?ita did actually find it. 



252 ANCIENT INDIAN CHRONOLOGY 

Nov. 10, 904 A.D,, 1 on which, at G.M.N. or 4-44 p.m. Morvi 

time, 

Mean Sun =234 22' 29" '34, 
Sun's Apogee = 83 9' 18"'32, 
Mean Moon =231 7' 21" '80, 
D. Node =246 7'31"'10, 

Lunar Perigee = 162 10' 10"'68. 

The new-moon happened at mean noon Morvi time, the 
magnitude of the eclipse as visible at the place was about '075. 
The beginning of the eclipse took place at 11-35 a.m. Morvi time, 
the end came about 12-45 noon Morvi mean time. Duration was 
about 1 hr. 10 min. 1 

Secondly, if we use the Khandakhddyaka constants, the 
ahargana becomes for 826 of Saka era 4-8 luuations= 87528. 
Henee the mean places with Lalla's corrections thereto, at 
G.M.N. at the same day, become: 

Mean Sun =228 18' 5", 

Moon -224 27' 36", 

D. Node =239 44' 56", 

Lunar Perigee =155 69' 47". 

It appears that this eclipse could be predicted by the method 
of the Khandakhadyaka. The gift made by tbis copper plate was 
probably a reward to the calculator of the eclipse. 

VI. The, Sixth Instance of Gupta Inscription Date 



In the year 156 of the Guptas, which was the Jovial year 
styled the Mahd vaiaklia year, the inscription records the date as 
the day of the 3rd tithi of the light half of Kdrtika. 

Now 156 of the Gupfea era =475 AJD. 

Julian days on Jan. 1, 475 A.D. =1894552, and 
1900 A.D. =2415021. 

Toe difference is 5*20469 days which comprise 14*24 Julian 
centuries + 253 days. We increase 520469 days by 12*25 days and 

1 The above circumstances of the eclipse have been calculated by my collaborator, 
Mr. N- C. Lahin, M.A. 

5 Fleet Gupta Inscriptions, page 104, the Khoh Grant. 



INDIAN EKAS 253 

arrive at the date, Dec. 20 ? 474 A.D., on which, at G.M.T. 6 hrs. 
or 11-4 a.m. Ujjayim M T., 

Mean Jupiter =170 54' 6'/.57, 
Mean Sun =269 47' IV M. 

Hence we calculate that mean Jupiter and mean Sun became 
nearly equal 289 days later, i.e., on the 17th September, 475 
A.D., at 6a.m. G.M.T., 

Mean Jupiter - 194 55' 84* '42, 
Mean Sun = 194 88' 19" 15. 

It is thus seen that the mean places would become almost 
equal in 6 hrs. more. For the above mean places, however, 
the equations of apsis for Jupiter and Sun were respectively 
-26'4"*01 and -145'2"'70. Hence their apparent places 
became as follows : 

Appt. Jupiter = 192 49' 30'/'41, 
Sun = 192 53' 16>/'45. 

Thus they were very nearly in conjunction at hrs, G.M.T. 
on the 17th September, 475 A.D. 

According to Brahmagupta, Jupiter rises on the east on 
getting at the anomaly of conjunction of 14. This takes place 
in 15 '5 days. Hence the date for the heliacal rising of Jupiter 
becomes the 2nd October, 476 A.D., at G-.M.T. 18 hrs., when 

Appfe, Sun =208 45', and 
,, Jupiter =>196 20 7 nearly. 

Thus Jupiter was heliacally visible about Oqt. 20, 475 A.D. 
The actual date of the inscription was Oct. 18, 473 A.D. 

Here on the day of the heliacal visibility, the sun 
was in the naksatra ViSakha, but Jupiter was 3 40' behind the 
first point of the naksatra division, the Vernal Equinox of 
the year being taken as the first point of the Hindu sphei'e. 
According to the rule of naming Jupiter's years as given in 
the modern Surya Siddhanta, XIV, 16-17, it was sun's naksatra, 
on the new-moon prior to October 18, 475 A.D. r the date of the 



254 ANCIENT INDIAN CHRONOLOGY 

inscription, which took place on Oct. 15-16 of the year, gave 
the name of the year. The suii would reach the naksatra 
Anuradha, and the year begun was consequently Mahd vaiakha 
year-of Jupiter. 

This inscription also shows that the Gupta era began from 
319 A.D. 

VII. The Seventh Instance oj Gupta Inscription Date 
IS ^.JTI t b*t^id ($\\) ^^li^jycBt STfTSfter^^r tf 4jHt 



The inscription records the date as the year 163 of the Gupta 
kings, the Jovial year called Mahd Asvayuja, the day of the 
2nd tithi of the light half of Caitra. 

The year 163 of the Gupta era or 482 A.D. was similar to the 
year 1941 A.D., and the date to March 30, 1941 A.D. In 1459 
sidereal years (1941-482 = 1459), there are 532909 days, which 
are applied backward to the 30th March, 1941 A. D., and we 
arrive at the tentative date of the inscription as March 8, 482 
A.D, On this date, ab G.M.N., we bad 

Mean Jupiter = 29 58' 8" '24, 
Sun = 347 12' 47" '11. 

Here, Jupiter's heliacal setting is yet to come in about 
30 days- Hence on April 7, 482 A.D., 

Mean Jupiter = 32 27' 46" '22, 

Sun = 16 46' 57"'02 at G.M.N. 

Thus the heliacal setting of Jupiter took place in two days 
more according to Brahrnagupta's rule on the 9th April, 482 
A. D., and the new-moon happened on the 5ih April, 482 A.D., 
when the sun was in the naksatra Bharanl. Hence the year to 
come got its name Igvayuga year. But the tentative date of 
the inscription was obtained as March 8, 482 A.D , which was 
21 days before the new-moon on about the 5th April, 482 A.D. 
This needs elucidation. 

i FleetGupta Inscriptions, p&ge 110, the Kh6h Grant II 



INDIAN EEAS 255 

Here by coming down by 30 days we arrive at the lunar 
month of VaiSaMa as it is reckoned now. But in the year 482 
A.D.,t.c., 17 years before the year 499 A.D., when the Hindu 
scientific siddhantas came into being, the calendar formation 
rule was different. In our gauge year 1941 A.D. the moon of 
last quarter got conjoined with Citrd or a Virginia, on the -20th 
Jan. before sunrise Hence as pointed out before in this gau-e 
year 1941 A.D. also, the lunar Agrahayana of the early Gupta 
period ended on the 27th Jan,, 1941 A.D. Thus the lunar month 
that is now called Pausa in 1941 A.D. waa called Agrahayana in 
482 A.D. Hence the lunar Caitra of 482 A.D. is now the 
lunar VaMaJcha of 1941 A.D. 

The date of this inscription is thus correctly obtained as the 
7th April, 482 A.D.\ the Jovial year begun was a Malia 
Itvayuja^ year. This- instance also shows that the Zero year 
of the Gupta era was approximately the same as the Chiistian 
year 319 A.D. 

VIII. The Eighth Instance of Gupta Inscription Date 



This inscription records the date, as the year 191 of the 
Gupta emperors, the Jovial year of Maha-eaitra, the toy of the 
third tithi of the dark half of lunar Maglia* 

We first work out the date on the hypothesis that the Gupta 
year was in this case also reckoned from the light half of lunar 
Pausa. The Gupta year 191, on this hypothesis, would be similar 
to the Christian year 1931, and the date of the inscription would 
correspond with March 0, 1931 A D. Now this Gupta year 
191 = 510 A.D., would be later tlan the time of Aryabhata I, 
viz., 499 A. D by 11 jears. 

The elapsed years (sidereal) are 1421, which comprise 17576 
lunations =519029 days. These days are applied backward to 
the date, March 6, 1931 A.D., and we arrive at the date. Feb. 
12, 510 A.D. 

1 Fleet Gupta Inscriptions, page 114, the Majligavam Grant. 



256 ANCIENT INDIAN CHRONOLOGY 

On this date, Feb. T2, 510 A.D., at G.M.N., we bad- 

Mean Jupiter = 158 8' 3"'87. 
,, Sun = 323 46'13'/'72. 

We find easily the sun and Jupiter had reached equality in 
mean longitude in 133*5 days before, when, at G.M.T. hr., 

Meau Sun = 142 54' 15'/*50 
Mean Jupiter = 142 52' 48*57. 

If these were the longitudes as corrected by the equations of 
apsis, then fche heliacal visibility would coine according to the 
rule of Brahmagupta about* 15 "5 -days later. Tha mean longitudes 
15.5 days later become 

For Sun = 158 10' 54" '21. 
For Jupiter = 144 KX 7'"25. 

Thes^, corrected by th? equations of apsis, become 

For Sun = 156 3' 27", 
For Jupiter = 146 16' 41. 

Hence the true heliacal visibility would coine in 4 days more. 
We have here (1) gone up by 183*5 days and (2) couie down 
by 15*5 days. On the whole we have gone up by 168 days or 5 
lunations + 21 t it h is. Thus on the day of the heliacal visibility 
of Jupiter, which came in lour days more, we would have to go 
up by 164 days=5 lunations +ntithis. This interval we have to 
apply backward to the llth tithi of Mdyha, and we arrive at the 
first day of BMdrapada. The date of the heliacal visibility would 
thus be Sep. 1, 509 A.D., and at G.M.N. the sun's true longitude 
would be 160 9' nearly, which shows that the sun would rtach 
the Hasta division. On the preceding day of the new-moon, the 
sun would be in the naksatm U. Plialguni, and the Jovial year 
begun would be styled Phdlguna or the Maha-phalguna year. 
This result does not agree with the statement of the inscription. 

It now appears that alter the year 499 A.D. or iryabhata I's 
time, the reckoning 01 the years of the Gupta era was changed 
from the light half of Paasa to the light half of Caitra, according 
to Aryabhata I's rule: 



Edhkriyd, 11, 



INDIAN BE AS 257 

" The yuga, year, month and the' first day of the year started 
simultaneously from the beginning of the light half of Gaitra." 

After the year 499 A.D. all the Indian eras slowly changed 
their year reckoning from the winter solstice day to the next 
vernal equinox day, i.e., the year beginning was shifted forward 
by 3 lunations. Hence in finding in our own time a year similar 
to the Gupta year, of times later than 499 A.D., we have some- 
times to compare it to the present-day Saka year and not to the 
Christian year. , 

Hence the year 191 of the Gupta era = the year 432 of the Saka 
era. In our times the Saka year 1853 is similar to the G-upta 
year 191 and the date of the inscription corresponds to Feb. 24, 
1932 A.D. The number of sidereal years elapsed up to this 
date =1421*= 5 19029 days, which applied backward lead t:> the 
date of the inscription as Feb. 2, 511 A.D. 

The date of the heliacal rising arrived at before was Sept. 1, 
509 A.D. The next heliacal rising would take place 399 days or 
13*6 lunations later. The date for it works out to have been 
Oct. 5, 510 A.D., and the sun had the longitude of 194 24' 51* 
at G.M.N. At the preceding new -moon, which followed the 
previous heliacal setting of Jupiter, the sun had the longitude of 
about 179^, and was in the naksatra Citrii or the Jovial year 
begun was Caitra or the Mahd-caitra year, as it is styled in the 
inscription. 

In the present case the year 191 of the Gupta emperors =432 
of the Saka emperors =510-11 A.D. Thus the year Zero of the 
Gupta emperors = 241 of the Saka emperors = 319-20 A.D. 



IX. 



The year and date as given in this inscription is 209 of the 
Gupta era, the day of the 13th tithi of the light half of Caitra. 
Following the Caitm-gukladi reckoning, the corresponding date in 
our time is the llth April, 1930 A.D. We have to apply 1402 
sidereal years or more correctly 17341 lunations =512090 days 
backward to this date of April 11, 1930 A.D. We thus arrive at 
the date of the inscription, March 19, 528 A.D, 
8814088 



288 



ANCIENT INDIAN CHRONOLOGY 



On this day, at G.M.N,, we had 

Mean Jupiter =347 37' 23 // *09, 

= 358 58' 52"'27, 



Hence 



Jupiter as corrected by 
the equation of apsis 

= 347 19', 
Appt. Sun=358 5'. 



Mean Sun 

Jupiter's Perihelion =350 51' 21"'61, 

Sun's Apogee -= IT 42' 66*, 

Eccentricity ='017301, 
Jupiter 's Eccentricity = *046 175. 

It appears that the heliacal rising of Jupiter would happen 
3 days later and the preceding new -moon happened 13 days 
before, i.e., on the 6th March, 52R A.D. . 

For on that date, at G.M.N. , we had 

Mean Sun =346 5' 8'9B, 

,, Moon =*343 5' 27"'90, 

Lunar Perigee =313 57' 86* '84. 

Sun's Apogee = 77 42' 56". 

The new-moon happened at about 8 hours later. The sun was 
in the naksatra Revati, and the Jovial year begun was Kfoaynga 
or the Malta Asvayuja year as the inscription says. 

Here the year 209 of the Gupta era=528 A.D. =year 450 of Saka era 
.'. the Zero year of the Gupta era =319 A.D.=:year 241 of Saka era. 

X, The Tenth Instance of Gupta Inscription Date 
The Nepal Inscription 



Hence 

Appt. Sun -349 4', 

,, Moon =345 43', nearly. 



Here the date is stated to have been, 386 of the (Gupta) 
era, the day of the first titlii of lunar Jyaisilia, the moon wasin the 
naksatra division Rohinl and the 8th part (mithilrta) of the day. 

The equivalent years are 627 of Saka era = 705 A.D.; we 
readily see that the corresponding day in our own time was, 
May 20, 1939. We arrive at the date, April 30, 705 A.D. 

(2) 



Now on April 30, 705 A.D., at 



G.M.T. hr., 

Mean Sun = 40 54' 10" '97, 

Moon = 62 0' 9" '07, 

Lunar Perigee = 322 39' 15* '02 

1 Fleet Gupta Inscriptions, page 95 f This inscription does not present 
peculiar feature* 



On April 29, 705 A.D., at 

G.M.T. Ohr., 

Mean Sun = 39 55' 2 // '64, 
Mean Moon 48 49'34 // *04, 
L. Perigee = 322 32' 33" '97 



INDIAN ERAS 250 



Thus on April 29, 705 A.D,, at G.M.T. hr., 

Apparent Sun = 41 12' 
Moon = 53 50'. 



Hence on this day, at the stated hour, the first tithi was 
over ; we have to deduct about 3 3' from these longitudes (mean) 
to allow for the shifting of the equinoxes from 499 A.D. The 
date of the inscription is thus April 28, 705 A.D. 

According to the Khandakhddyaka calculations the aliargana- 
at the midnight (mean) of Ujjayim of April 28 = 14617, .In 
order to have the mean places at the G.M.T. Olir., of 29th 
April, we have to take the aliargana = 14647 days + 5 hrs. and 
4 min. The mean places are 



Mean Sun = 36 52' 12", 

Mean Moon = 45 43' 58", 

Sun's Apogee = 77 0' 0", 



Hence 

Apparent Sun = 38 16' 23", 
Moon = 50 44' 30". 



Lunar Perigee - 318 56' 2". 

Note : To the Khandakhddyaka mean places, we have applied 
Lalla's corrections which are well-known in Hindu Astronomy, 

Hence on the 29th 'April at G.M.T. hr. = 5-4 a.m. of 
Ujjayim mean time, the first tithi was over, the sun was in the 
naksatra KrttiM and the moon in the naksatra division Bo/iim, 
which extends from 40 to 53 20' of the Hindu longitudes. 
The date of the inscription was the previous day, the 28th April, 
705 A.D., as has been shown before. 

Now Gupta year, 386 = Saka year 627 705 A.D. 

/. Gupta year, Zero = Saka year 241 = 319 A.D. 
XI. The Eleventh Example of Gupta Inscription Date 



The date of the inscription is the Gupta year 199, the 
Mahd-marga Jovial year, the" day of the lOlh titlii of lunar 
KflrMfca, which corresponds to Nov. 21 of 1939 A.D, of our times. 
The elapsed siderial years to this date - 1421 - 17576 lunations 
*= 519029 days. 

l Mpigraphica Jndioa, Vol, "VIII, pp. 254 t seq. 



260 ANCIENT INDIAN CHRONOLOGY 

Hence the date of the Inscription was Oct. 29, S18 A.D 
On this date, at G.M.N., 

Mean Jupiter = 62 34' 9'/'59, 
,, Sun 219 & 50*' 17, 
,, Moon = 332 32' 20* '47, 

Now 169 days before Oct. 29, 518 A.D., the true longitudes 
were on May 13, at U.M.T. 6 hrs., for 

Jupiter - 58o'16'", 

Sun = 52 55' 15", 

and these are practically equal. Hence according to Brahtna- 
gupta's rule Jupiter should rise heliacally 15*5 days later, 
i.e., on May 29, 518 A.D. But on May 24, 518 A.D., 
the mean sun had, at G.M.N., the longitude of 63 22' 54" 
and the mean moon at the same hour, the longitude of 50 40' 6". 
Thus the new-moon came on the day following, the sun having 
a small positive equation. The ne^-moon-sun was in the 
naksatra, division Mrgasiras ( 53 23' to 66 40' of longitude) , 
and the Jovial year begun was Mdrga or the Malia-m&rga year 
as the inscription says. 

Tkus the Gupta year, 199 = 518 A.D. 
.'. Gupta year, Zero = 319 A.D. 

XII. Tioelfth Instance o] Gupta Inscription Date * 

Epigraphica Indica, VoL 21, Plate No. 67 The Navagrara 
Grant of Maharaja Hastin 



[ 

The year 198 of the Gupta era or 517 A.D., is called Mahd- 
dtvayuja year. We find that on April 7, 517 A.D., at U.M.T. 
6 hrs., 

Mean Sun - 16 51' 25" '67, 

Moon 15 55' 0^42, 

Lunar Perigee = 280 1' SO'^O, 

. A. Node = 2 58' 2Q' / '27, 

, Mean Jupiter = 14 58' 46^85. 

* Zielhorn's approximate date was 518 A.D., Oct. 15 or September 15 Epigra- 
phies Indica, VoL VJIT* p^ge 290. 

* Commuijicated by Prof. D. K. Bhandarkar, 



INDIAN E1US -2<:1 

This was the day of the new-moon with Jupiter at the 
position very near to conjunction and consequently of heliacal 
setting. The new-moon happened in the nnksatm B/ZKJW/I. 
Hence the year is called the jtfahd-dsvayuja year. 

Here also the Gupta year, Zero=319 A.D, 

Conclusion 

We have here proved, from 12 or 11 concrete statements found 
in the inscriptions, which have used either the Gupta or the 
Valabhi era, that 

(1) The Gupta and Valabhi eras were but one and the 
same era. 

(2) It was most probable that the era in question had been 
originally started by the Gupta emperors and was given nuw 
name by the Valabhi princes who were vassals of the Gupta 
emperors. 1 

(3) The date from which the Gupta era was started was 
Dec. 20, 318 A.D., when began the Zero year of the era i'rom 
the day of the winter solstice. 

(4) That the Gupta era agrees with the Christian era from 
319 A.D. till about 499 A.D., the date of Aryabhafa I, up to 
which the year reckoning began from the light half ol Pansa. 

(5) Prom some year which was different for different 
localities after 499 A.D., the beginning of the year was lifted 
forward from the light half Pausa or the Winter Solstice day to 
the light half of Centra, conformably to Aryabhata I's dictum 
of beginning the year from the Vernal Equinox day. This 
produced, in 'indian calendars, " a year of confusion," as it is 
called in calendar reform. One year of the Gupta era and 420 of 
the gaka era were thus reckoned as consisting of 15 or 16 luna- 
tions. This is evident from the inscriptions dealt with as 
Nos V VIII, X and XL This change has been noticed in 
the inscriptions of those localities where Aryabhata I's reputation 
as the foremost Indian astronomer had been unquestionably 
accepted. la such cases the Gupta years correspond more 

i meet-Gupta Inscriptions, Plate No. 18, the Mandasor Stone , Inuripiioo of 
and Bandhuvarman discussed ia Chapter XXIV on the Sa>n*at era. 



262 ANCIENT INDIAN CHRONOLOGY 

conformably to the Caitra-Suklddi Saka years and that the Zero 
year of the Gupta emperors is taken as the Saka year 241 (Caitra- 
Si&huli) which is the same as the Christian year 319-20 A.D. 

To sum up : The Zero year of the Gupta era was originally 
the same as the year 319 A.D., and in times later than 499 A.D. 
this Zero year was in some cases taken as equivalent to 
319"*20 A.D. Further the Gupta and Valabhi eras were the 
same era. It is hoped that further speculations as to this era 
would be considered inadmissible. 



CHAPTER XXYI 

TIME-INDICATIONS IN KILIDI8A 

As to the date of Kalidasa, the greatest of our Sanskrit poets, 
most divergent views have been held by different researchers. 
According to Maxmiiller, Fergusson and H. P, Sastri, Kalidasa 
lived about the middle of the sixth cientury A.D. On the other 
hand, Macdonell, Vincent Smith and A. B. Keith have held that 
the poet flourished about the time of the G-upta Emperor Chandra- 
gupta, II, the first Indian monarch who, on epigraphic evidence, 
is known to have assumed the title of Vikramaditya (ca. 380-415 
A.D.) This is of course on the assumption that Kalidasa adorned 
the court of a king named Vikramaditya of Djjayini, a tradition 
which appears to be of very doubtful value. Then again Prof. 
S. Bay, 1 Sten Konow, Chatterjee and other Sanskritists of the 
old school have identified the now known Vikrama Sathvat, with 
the era alleged to have been started by Vikramaditya of Ujjyaim 
and have tried to assign to the poet the first century B.C. But 
epigraphic and other evidences are, so far as I am aware, against 
this identification, as the original name of this Sam vat era was 
'Malavabcla* or even Krta era. We do not yet know when the 
original name of the era was changed into Samvat era, 

As no definite epigraphic evidence about the date of Kalidasa 
is forthcoming, such differences of opinion are quite natural, 
and any attempt to throw fresh light on the problem from a new 
point of view will probably be welcomed by scholars. 

In this chapter we have tried to show thafc the great poet 
was thoroughly conversant with the Hindu Siddhdntic (scientific) 
astronomical literature, such references being found scattered 
throughout his poetical and dramatical works. These references 
have not been, as we shall see, correctly interpreted by his many 

i Prof S Bay's paper, 'Age of Kalidasa,' J.R.A.8., Btngal, 1908. Compare 
also the Allahabad University Studies, Vol. 2, 1926, < On the Date of Kahdasa " 
by Chatter joe. 



264 ANCIENT INDIAN CHRONOLOGY 

commentators including Maliinatha. The reason is obvious. 
These commentators were primarily rhetoricians and not experts 
in astronomy ; hence they failed fco get at the propsr meaning of 
the passages and thus by their failure in this respect, have only 
( darkened counsel by their words ' in their commentaries. We 
take these references one by one ; we shall try to interpret them 
correctly and ascertain their chronological significance. 

(a) The first reference is 

Naksalra-taragraha-samkula-pi jyolismati candramasaiva ratrih 

Bagho, VI, 22. 

Here the word c tar agr alia' is a Hindu astronomical term not 
recognised by Maliinatha. It means 'star-like planets/ viz., 
Mercury, Venus, Mars, Jupiter and Saturn in contradistinction to 
the Sun and the Moon which possess discs ; the Hindu scientific 
astronomers throughout maintain this classification (cf. Panca- 
siddhantika, XVIII, 61 ; the Kryabhatlya, Go/a, 48 ; Modern 
Sfirya Siddhanta, VII, 1, etc.). Here Maliinatha splits up the 
compound word as 'naksatra' + tara' + < graha > . This sort of 
"interpretation is apparently against the meaning of the poet. 

(6) That Ealidasa was a keen observer of the first visibility 
of crescent is evidenced by 

(f J Netraih papus trptimanapnuvadbhir 

Navodayam ndthamivausadhinam Baghu, II, 73. 
(ii) NidarsSayamasa vi^esadr^yain 

indurh navottltanamivendwnatyai Raghu, VI, 31. 

In these Instances we have the expressions whicb are 
equivalent to "the newly risen lord of the osadhis 9 and 'to newly 
risen moon'. 

(c) We have further in Kalidasa 

Tisrastri-lokiprathitena Rardhamajena marge vasat Irusitva 

Tasmadapavartata Kundinesah parvafcyaye soma ivosnara^meh* 

Eaghu, VII, 33. 

Here the poet says that in Aja's return journey to the city of 
Ayodhya, the prince of Vidarbha (his brother-in-law), unwilling 
to part company of him as it were, accompanied Aja for three 
nights, just as the moon, as if unwilling to part company of the 



TIME-INDICATIONS IN KILIDISA 265 

sun at the conjunction, remains invisible for the maximum period 
of three nights and then separates from him, This interpretation 
makes the figure a purnopunid or a complete similitude. Hence 
Kalidasa was also an observer of the fact that the moon's 
maximum period of invisibility lasts for three nights. Mallinatha 
here fails to interpret the simile in Kalidasa. 

(d) Again \*e have the line 

Esa carumukhi, yogataraya ynjyate taralavimbaya Sasf 

Kumara, VIII, 73. 

'This Moon, lovely one, is getting conjoined with the 
liquid bodied, il junction-star' ' of this night.' 

Here we have the two words 'yogatdrd* and 'taralavimbaya'; 
the first one means any one of the several 'stars' with which 
the moon gets conjoined in her 'sailing' through the sky in the 
course of a sidereal month. Mallinatha makes a muddle of 
the whole thing when he says that the moon is always 
accompanied by a particular star in all nights (pratyahaihyaya 
yujyale sd yogatdrd). Again the word 'tarala-viwbaya* means 
liquid-bodied, and not- as Mallinatha expounds it. A verse of 
the Stirya Siddlidnta, as quoted by Bhattotpala (966 A.D.) in 
the commentary on the Brhatsanilntd of Varahamihira, runs 
thus : 

Tejasaih golakah suryo graharksanyambugolakah 

Prabhavanto Li dryante sfiryarasmividlpitah 

Brhatsamhita, IV. 
(first cited by Diksita, in his work Bharatiya Jyotihsastra, p. 179). 

'The sun is a sphere of energy, the planets and stars are 
spheres of water, they are seen shining by being illumined by 
the rays of the sun.' 

This evidence shows that the poet had studied the Siirya 
Siddhanta as known to Bhattotpala, and used the word 'tdrala- 
vimbayd* in the strict Siddhdntic sense. 

(e) Another very important astronoaiical passage in Kalida-s^ 
is 

Agastyacihnadayanat samlpaiii diguttara bhasvati sannivrtte 
Ananda^Itamivavaspavrstim liimaprutim haimavatim sasarjn. 

Raghu, XVI, 44, 

84 H08B 



266 ANCIENT INDIAN CHRONOLOGY 

or, 'when the sun neared the solstice (summer solstice) which was 
the place of Canopus, North caused a, flow of ice from the Hima- 
layas, which was like a delightfully cold shower of rain.* 

Here also Mallinatha, owing to ignorance of Siddhantic 
astronomy, fails to interpret the phrase 'Agastya cihna, 9 which 
cannot but mean the ecliptic place.of Ganopus. His meaning of 
the phrase is * the southern solstice ' (the winter solstice). The 
poet in the very preceding stanza speaks of the advent of summer 
at the beginning of which the sun had already left the winter 
solstice four months before, and was only 60 distant from the 
summer solstice. The phrase in question undoubtedly means 
the summer solstice. As to the Agastya's (Canopus) 'polar' 
longitude and latitude the astronomical siddhdntas say : 

In Modern Surya Siddlidnta (VIII, 10) we have * Agastyo 
Mithunantagah'. 

In Paficasiddhantika (XIV, 10) we have 'Karkatadyat'. 
From the above and other works we learn of Ganopus' s place as - 

Polar longitude Polar latitude ' 

Modern BQrya Biddhanta ... 90 S 80 

Paftcasiddh&ntiTcS, (550 A.D.) ... 90 S 75 20' 

Brahmagupta (628 A.D.) ... 87 S 77 

Lalla (748 A.D.) ... 87 S 80 

From the above 'polar' longitudes of Canopus it' appears that 
both Varaha and Kalidasa belonged to the same school of 
Siddhantic teaching. The date of the earliest form of the 
Modern Surya Siddhanta is most uncertain. It may even be 
about 560 A.D. as estimated by Burgess. 1 

(/) The poet is almost enamoured of the event of the sun's 
reaching the summer solstice when the tropical month of Nabhas, 
the first of the rainy season, began. The poet says in Ragliu, 
XVIII, 6: 

Nabhafearairgltayjadah sa lebhe 

nabliastalasyamatanum tanujam ; 
Khyatam nabhahfiabdamayena namna 
kantarh nabhomasaniiva prajanam, 

1 If ib was recast first into the modern form by La,tadeva (427 Saka year or 
505 A.D ) as recorded by Alberuni (India , VoJ. I, XIV, p. 1), the date may go up to, 
aay, about 510 A.D. and not earlier. 



TIME-INDICATIONS IN KILID1SA 267 

'The king (Nala), whose fame was sung by the denizeijs of the 
sky, got a son of the same colour as the sky who became known 
by the name of Nabhas and was to his people, as pleasing as 
the month of Nablias, the first of the rainy season. 

(g) Kalidasa has again in Racjlni, XI, 36 

Tau videhanagarmivasinaiii gam gataviva divah punarvasu 
Manyate-sma pivatam vilocanaih paksmapatamapi 

vaftcanaiii vuanah. 

'The princes, Kama and Laksinana, as they stood before the 
people of the city of Videha, appeared as charming as the two 
stars Castor and Pollux of the naksatm Punarvasu. As they 
drank with their eyes the beautiful forms of the princes, their 
mind took it a disappointment that their tired eyelids fell 
preventing a continuous vision.' 

To the poets why the stars Castor and Pollux were so charming, 
was that the sun reached the summer solstice at a place near 
to them, and the bursting of the monsoons took place. In the 
annual course, the star Castor's place is first reached by 
the sun. We shall not, therefore, be very wrong to assume that 
the poet indicates that the summer solstice of his time lay very 
near to the place of this star. The time when the summer 
solstitial colure passed through it was 546 A.D. It remains yet 
to be examined how far it indicates the date of the poet. 
Enough has been shown to establish, I trust, that Kalidasa was 
well trained in the Siddhantic astronomy of this time, was 
himself a keen observer of the Heavens and specially of the moon's 
motion amongst the ecliptic stars. We now proceed to consider 
the other Lime-references in Kalidasa's works. 

Other Time-References in Kalidasa 

The first of these time-indications is derived from the Mcgha- 
data. The stanzas in Part I, 1-4, say that the exiled Yaksa 
addressed the cloud messenger on the first or last day of Isadha ; 
' prathama' and ' prasama ' are the two variants of the text. 
In the edition of the Meghaduta by Eullzsch, the commentator 
Vallabhadeva accepts the reading pratamadtom and discard* 



208 ANCIENT INDIAN OHEOXOLOGY 

the other, and Mallinalba on the other hand accepts the reading 
prathamadivaxe and rejects the other. We have to settle 
which is the correct reading. We learn from Part II, verse 
49, that the Yaksa's period of exile would end in 
four mouths more, when Visnu would arise from hi a bed 
of the serpent Sesa ('Sapanto rne bhujagaj5ayana.dutth.ite 
sjlrngapanan, sesanmasan garaaya caturo, etc.'). The date 
for this last event being the day of the llth Lithi of lunar 
Kurttika, four lunations before it was the day of the llth tithi 
of lunar Isadha. Hence the day on which the Yaksa is said to 
have addressed the cloud messenger was that of ^the llth tithi 
of lunar Asddlia. As this day can never be the first or the last 
day of the lunar Asddha, and as this day can never fall on the 
first day of solar Asddha 3 the real reading of the text is * P-rasama- 
divase ' and not ' Prathauiadiuase,' the month -being the solar, 
and never the lunar, Asddha. Thus the day on which the Yaksa 
is made to address the cloud messenger was 

(1) The day of the llth tithi of lunar Asadha. 
(2j The last day of solar Asadha. 

(3) The day of the summer solstice, as this was the day for the 
bursting of the summer monsoons marked by the first 
appearance of clouds. Here Kalidasa says e that a huge 
mass of the first -rain clouds hanging from the side of the 
hill looking like a ,fully developed elephant, burying its 
tusks on the hill side/ * nieghamaslista-sanurn vaprakrida- 
parinata-gajVpreksaijiiyaih'dadarsa/ as the poet has it. 
The next day itself was the first day of Ndbhas, the first 
month of the rainy season. The poet says that this month 
was imminent or ' pratyasanne Nabhasi ' when the Yaksa 
addressed the cloud. With the learned Sanskrit authors, 
the summer solstice day was the true day for the 
bursting of the monsoons. On this point c/ t the 
Ramayana> IT, Oh. 63, St. 14-16. 

The poet here in the Meghaduta "has recorded a notable 
astronomical event of his time. We have already seen that 
he has indicated the position of the summer solstitial colure 



TIME-INDZCATLONS IN KALIDASA 26U 

as almost passing through the star Castor, that this time 
was about 546 A.D. Now examining the period from 541 to 
571 A. D., we find that the day on which the three conditions 
tabled above were satisfied was : 

The 20th June, 541 A.D., on which, at Ci.M. Noon or the 
Ujjayim mean time, 54 pan. 

Klianrlakluld} aka Moderns 

** 

True Moon = 220 1' 227 2' 

True Sun = 89 38' 90" V 

Note. The Khandakluldyalia is an ashonomical compendium 
by Brahmagupta, dated 665 A.D., in which he sets forth the 
drdliardtrika sybtem of astronomy as taught by Iryabhata 1. 
Varaha, in his Suryasiddhdnta, has borrowed wholesale from 
Iryabhata I, but without mentioning in any way the source he 
is a borrower from. 1 There are indeed only two systems of the 
Hindu Siddhantic astronomy, the d-nlharatrika and the audayila. 
To the former class belongs also the Modern Surya Siddliwita, 
to the other class fall" the Iryabhatlya, the Brdhmaspliuta- 
siddlianta of Brahmagupta (628 A.D.) 5 the Sisyadlritrddhida of 
Lalla (74S A.D.), the SiddlidntaitMi&ra .of Srlpati and the 
Siddhdntasiromuni of Bhaskara I. 

Here, according to HbeKhanda'khddyuka 9 Moon Sun =13623 / ; 
the eleventh tithi was over about nine hours before, f.e., at about 
8 a. in, in the morning, and the first day of Kablias was the next 
day, and that this date of June 20, 541 A.D., was the true last 
day of the solar Isadha. The sun's longitude according to the 
modern constants shows the day as the true day of the summer 
solstice of the year. This reference thus indicates the time of 
Kalidasa as about 541 A.D., which is not very different from 546 
A.D. .obtained before. 

The second of these time-indications is derived from our poet's 
drama, Abhijnana6akuntala VII, 91. Here Ealidasa employs 



1 P. C Sengupta, Translation of Uie Kliaydakhadyaka, the introduction, Calcutta 
University Press, 1934 A.D. 



270 ANCIENT INDIAN CHBONOLOGY 

an astronomical simile to describe the final union of Dusyanta 
with Saktwtaln. The prince thus speaks to his consort : 
Prije, Smrtibhinnamohatamaso 

Distya pratnukhe sthitasi sumukhi 
Uparagante sasina 

Samupagata Rohhil yogam. 

' It is by a piece of good lack, my lovely darling, that you 
stand before me whose gloom of delusion has been broken by a 
return of memory. This has been, as it were, the star Rohinl 
has yot conjoined "with the moon at the end of a total eclipse.' 

So far as we can see, our poet again uses another specially 
noticeable astronomical event of his time for a simile. A total 
eclipse of the moon happened according to Oppolzer's Cannon der 
Findcmesse on November 8, 542 A.D., with the middle of the 
eclipse at 17 hours 5 mioutes of G.M.T. or the Ujjayim mean time 
*22 hours 9 minutes : the half durations for the whole eclipse 
and the totality were 112 minutes and 51 minutes respectively. As 
to the magnitude and the half durations, I trust, Oppolzer's book is 
correct, although not based on the most up-to-date astronomical 
constants. The authorities for his longitudes were Leverrier 
and Hansen ; thus the beginnings and ends are not very correct- 
as set forth below : 

On November 8, 542 A. D., at 17 hours 5 minutes, G.M.T., 
we have 

Newcomb and Brown Leverrier and Hansen 
Apparent Sun ... 228" 28' 49" 228 28' 46" 

Apparent Moon * ... 4816 / 41 //1 48 26' 3" * 

Thus according to the most up-to-date authorities, 
Moon ~ Sun = 12' 8", while according to Oppolzer's authorities 
the same = 2' 43*. The difference of 9' 25" would be gained 
by the moon in 19 minutes more. Consequently the beginnings, 
the middle and the ends have to be shifted forward by 19 
minutes. The eclipse thus began most conveniently 'at 8-36 p.m. 
and ended at hour 20 minutes a. m. of the Ujjayini mean time 
on November 9, at a very favourable time for the observation 

1 Corrected by 12 principal equations. 



TIME-INDICATIONS IN K1LIDISA 271 

of the conjunction of the moon with the star Rohim (Aldelaran), 

an 1 at this instant- 
Apparent mSon ... ... ... 49 31' 10" 

Longitude of Rohiril (Aldebaran) ... ... 49 30' 11* 

Latitude of Rohlni (Aldebaian) ... ... -5 28' 17" 

The moon at the end of the eclipse had almost complete 
equality in longitude with the star Aldcbciran or Rohim, as could 
be estimated by producing the line of the moon's cusps formed 
at the eclipse some time before its end. 

The date of this peculiar lunar eclipse, viz., 8-9 Nov., 542 A. D. 
confirms the dates 516 A.D. and 541 A.D. .as obtained before. The 
period in which Kalidasa in all probability observed these three 
astronomical events, which he has recorded in his work in his own 
way, runs from 541 to 546 A.D. The events thus tend to place 
Ivalidasa in the middle of the sixth century A,D. 

In the previous reference ( from the Meghaduta) we have 
shown before, that in the phrase ' Asddhasya prahmadivase,' 
the word 'Asddha' is to be taken in the sense of the 'solar' 
and not of the 'lunar' month of Asadha. 

This interpretation makes the date of the poet later than the 
date of the starting of the Hindu Siddhantic astronomy. I have 
not as yet come across any mention of solar months in Indian 
epigraphy. That the Hindu siddhdntas date from that epoch at 
which the planetary mean places (or even apparent places) are 
almost all equal to the tropical mean longitudes as calculated 
from the most modern astronomical constants, is -the sole test 
by which it can be ascertained. Aryabhatal indeed makes 
his epoch 3,600 years after the Kali epoch of 3102 B.C., Feb. 17, 
24 hours 01 February 18, 6 hours of Ujjayim mean time. The 
date and hour we arrive at is 

March 21, 499 A.D,, Ujjayinl mean midday. The mean 
longitudes are shown in the following table 1 : 

Compare also the Table on page 38, 



ANCIENT INDIAN CHRONOLOGY 



Planet 


Irdha- 
ratrika 
system 


Audayika 
system 


Mod. S, 
Siddhanta 


Mean Trop. 
longitudes. 
Moderns 


Error in 
irdha- 
ratrika 


Errors in 
Audayika 


0) 


(2) 


(3) 


(4) 2 


<5) 


* (6) 


(7) 


Sun 


O'O" 


0* O'O" 


O'O" 


359 42' 5" 


+17'"55" 


+17' 55" 


Moon ... 


280 48' 0" 


280 48' 8" 


280 48' 0" 


280 24' 52" 


+23' 8" 


+23' 8" 


LA. Node 


352 12' 0" 


352 12' 0" 


348* 20' <T 


352 2' 26" 


+9' 34" 


9' 14" 


L. -Apogee 


3542'0" 


35 42' 0" 


34" 56' 43" 


35 24' 38" 


+17' 22" 


+17' 22" 


Mercury 


180 O'O" 


186 O'O" 


198 7'48' 7 


138 9' 51" 


-180' 51" 


+170' 9" 


Venn s ,.. 


350 24' 0" 


356 24' 0" 


352 48' l>" 


356 7' 51" 


+16' 9" 


+16' 9" 


Mars ... 


7" 12' 0" 


7 13' 0" 


9 C 48' 0" 


6* 52' 45" 


+12' 15" 


+19' 15" 


Jupiter ... 


186 O'O" 


187 12' 0" 


186 0' 3" 


187 10' 46" 


-i0'47" 


+1' 12" 


Saturn ... 


49 12' 0" 


49 12' 3" 


50 24' 0" 


48 21' 13" 


-50' 47" 


+50' 47" 



The mean e planets ' of the ardharatrika system are the same 
as taught by Varaha in his so-called Stiryasiddhanta. The date 
of the Modern Surya Siddhanta as judged by a similar test is 
put at 1091 A.D, by Bentley, which cannot be set aside as un- 
acceptable (Calcutta Univer&ity reprint of Burgess's translation, 
page 24). The reader may on this point compare Dlksita's work, 
the Bharatiya Jyolihsastm, page 200, 1st edn,, and also my 
article, 'Hindu Astronomy 1 in the journal Science and Culture 
for June, 1944. 

The planetary position as in cols. (2), (3) and (5) are in 
general agreement, excepting in thai of Mercury, where the 
error is respectively -3 and +3 C nearly in the above two 
systems. The next great difference of +51' occurs in the" mean 
place of Saturn ; in almost all other cases the Hindu mean places 
(or more correctly Aryabhata's) are almost the same as calculated 
from the most modern constants. Hence there should 
not be any doubt as to the date from which the Siddhantio 
calculations were started that date must be March 21, 499 A.D. 
The Hindu rule for calculating what is called Ayanam$a> or the 

3 The Modern Surya SiddJwta longitudes are for 12 hours 33'6 minutes of 
0. M. Time. 



TIME-INDICATIONS IN KILID1SA 273 

distance* of tbe Iss point of the Hindu :-pWe from the vernal 
equinox of date, also accept- this as tiia date \vli3n t ! ie two 
points were coincident. TiK-re is ano:"i2' -l:te al-'o, e/s., 441 of 
Saka era or 522 A.D. , called the Bhar:. y:ir, iVjm which also 
the Ayanlmsa is calculated. Thus we cr.vluiie that as Kalidapa 
means the sohr rnont i of AstJlia In ;he phrase * As. Idhasya 
praiamadtvase,* his date ciirmct be earlier than 499 A.D., or 
eve'i 52:2 A.D. It wa ; from alnut these date? that the Hjnlu 
signs of the zodiac were for p.ed and solar months for the different 
signs of the zodiac came to he calculated in the Hindu calendar, 
ia the fonn of transits of the sun from one sign of the zodiac 
to thp next. 

As to the date of Kalidi?a, we have, as pet forth above, the 
first time-indication in which he hints that the summer 
polptitial colnre of his time passed almost straight through the 
star Castor, for which the date has been worked out as 546 A.D. 
Secondly, the ristronomical event of the combin tion of the 
last c1?iy of solar Astldha, the day of the llth titlii of lunar 
Asfidliu and the day of the summer solstice falling on tlie Fame 
day ha-* siven us Ih3 date 541 A.D., June 90 Thirdly, tie date 
of (he total lunar eclipse, wliich was most favourable for the 
observation of the moon, being conjoined with the star Rolrini 
(Aldclnran) at its end, has led to the data Nov. "9, 542 A.D., 
so closely converging to the preceding dates. All these 
findings finally fix the da'-e of the greatest of the Sanskrit 
poeiR at about the mid-lie of the pixth century A.D. We have 
also *howw tlmt ns the dnte of all the extant Hindu scientific 
sitld'nrnitas cannot he earlier than 499 A.D., March 21, and 
that it may even be, Inter than 52 A D., the da*e of Kalidasa 
cannot but he about .Ul-51t5 A,D.,as he u-c-s the phrase. 
' Ast Idhasya pra&amadwase.' which cannot but mean the last 
date 'of the solar month of Xstldlia. Even by the learned 
ancients puch an expres?ion, indicating the use of a solar month, 
waB not poFsible before the time of Iryabhata I, so far as I have 
come to learn from my stu4y of Hindu astronomy for more 
than three decades. Before 499 A.D. this science was in the 
amorphous state. The Jyotisa Vedamga calendar litis a tradition 

35-1 10RB 



274 



ANCIENT INDIAN CHEONOLOGY 



that the fiye-yearly Vedic calendar was started from about 
1400 B.C., but we have evidence to show that this calculation 
was never extended beyond five years. The late Mr. S B n 
Diksita, in his Bharatiya Jyotihsdstra, page 125, has quoted a 
verse from the Mahdbharata, $anti> Ch. 301, 40-47, in which 
we find that the calendar-makers or the wise men found ' omitted 
years, months, half lunations and even days ' in trying to follow 
the fi^jp-yearly luni-soiar cycle. It is a pity that nothing is on 
record to show when arose occasions for such adjustments 
being made and how these wise men failed to find the J9 years 
or the 14J years as the more correct luni-solar cycles by these 
processes. In these calculations there was no use of the signs 
of the zodiac and of no other planets except the sun and the 
moon. When Ealidasa uses the solar month, we have an indica- 
tion of the existence of crystalline state of Hindu astronomy 



i 




The same 












Tropical 


referred 










lljjaini 


longitude 


to the M.Y. 


Khanda- 


Kf anda- 


Cur- 


Rummer 


Date. Mean 
Time 


of the sun 
Moderns 


Equinox of 
March 21, 


khauyaka. 1 
True Sun 


khadvaka. 
True Moon 


rent 
tithi 


Solstice 
on 


hr. 




499 A.D. 










188 AD., 6a.m. 


?950'3S" 


3*4 9' 7" 


3'512'4C/' 






The Gth 


June 23 












of so'ar 


i 












Sravana. 


802A.D., : 


89 49' 10* 


3'2'27'52" 


3 '3 33' 18" 






The 4th 


June 22 , 












of solar 














Stavana. 


416 A,D., ' ,, 


89 44' 42" 


3'053'34" 


3 f l 26'26^ 






The 2nd 


Juue21 












of* solar 


427 A. ' t , 


89 6' 41" 


3'0 G'24" 


3 f O*37'19 w 


7"irM'3'2 // 


llt,h 


The 2nd 


June 21 












of solar 














Sravana. 


4fllA.D. f 24hrs. 


90 2' 0" 


8' 6 14' j 3" 


3 g U37'28" 


7'ir43W 


IHh 


The Ia*Bt 


June 20 












day of 














solar 










* 




5 sad ha. 



1 We have followed the Khantlakhadyaka of Bra'uiiagnpta in the calculations as 
no better or more reliable ancient works a.re known to us. 



TIME-INDICATIONS IN KALIDISA 



215 



of the time of Aryabbata I, winch dales from March 21, 
499 A.D. 

For finally settling this point, there should be forthcoming 
epigraphic evidence as to the use of tLe solar months by the 
learned Indians before the time of Srjabhala I. So far as I 
Lave eeen, I have not come across any earlier use of solar . 
months in any epigraphic statements: the dates are invaiiably 
stated in terms of the lunar months alone. If we want to 
explore the possibilities of a repetition of the Mtgliadtlia astio- 
nomical event in the peri -,] from 188 A.D.5-11 A.D. , we find 
that the only previous date for its occurrence was 484 A.D., as the 
above calculations will show : 

We refer the tropical longitudes of the sun to the mean 
vernal equinox of March 21, 499 AD., as this was the true 
date fiom which the Hindu Siddhdntic calculations are really 
started and the mean vernal equinox of 'he date is the true first 
point of the Hindu s-phere. 

It apears from the above calculations that the date ^541 A.D., 
June 20, may be raised by the -hort interval of 57 years to the 
date 481 AD., June '20, from a pure astronomical finding taken 
singly. There are, however, at present no good reasons even 
fo/tbie small shifting of the date already arrived at, as explained 
already. It becomes quite inadmissible on a consideration of 
our last reference in the same way. 

In the list of total eclipses of the moon visible in India and 
happening near the star Aldebaran as given in Oppolzer's 
Cannon *der Finstcrnesse during the period from 400 AD. to 
COO AD., we have only the following: 



Pate 


Middle of 
Eclipse 0- M,T. 


Half duration lor 
\vbo1c eclipse 


Half duration 
for totality 


459 A.D., 


October 27 


14 hrs. 30 mins. 


111 mins. 


50 mins. 


477 A.D., 


November 6 


23 hrs. 21 ii.ins. 


Ill mins. 


50 inins. 


542 A.D. . 


November 8 


17 bra. 5 mine. 


112 mins. 

^^^a 


51 mins. 



As to the eclipse of date October 27, 459 A.D, there cannot 
be any conjunction of the moon with the star Rohim (Aldebaran) 



276 ANOIEN1 1 INDIA S CMRONOLOJY 

at its end, as both the date anl the hour are unfavourable. As 
regards the eclipse of November 6, 477 A.D., it would end, 
accoiding to Oppolzer's CumoH, in the naxt day a', the Ujjayini 
mean time 6 h:<urs 16 minutes. But as his authority for the 
longitude of the moon was Hanseii, the end of the eclipse 
would have to b* shifted fo"<w:l by :2.) minutes He, 126 the 
end of the eclipse wo'ild be :it G h mrs 30 minutes of the Ojjiyini 
mean time. The sunrise works out as '* hoars 27 minutes of 
U, M. time, i.e., the eclipse did not end before the sunribe oa 
the day iu question. Kiilidasa e-aild not possibly mean this 
eclipse in Irs simile in the jSakimtala. 

The peculiar lunar eclipse on 89 November, 54-2 A.D , and 
the sun's turning south on June 20, 541 A.D., taken together 
thus fixes the date of Kalidata about the middle of the sixth 
century A.D., and this leads to the conclusion that the great 
poet and the ablronomer Varaha were contemporary. We have 
also pointed out already that Kalidasa indicates that the summer 
solstitial -colure of his time passed through the sfar Castor for 
which the date becomes 546 A.D. 

As to Yaraha's date, we know that he flourished ahout 
550 A.D., as he mentions Aryabhata I (199 A.D.) by name 
and is himself mentioned by Bralrnngupti (6i28 A.D.). Amaraja, 
the commentator of the Khandukhadyaka of Brahmagupta, 
says that Varaha died in 587 A.D. Hence the two of the 
'nine gems' of the tradition may be contemporary, but that 
they all belonged to the court of the King VikramS'Utja may 
be wholly wrong. 

As far as I have been able to ascertain, the verse which 
records the tradition, m%> : 

Dhanvantan-Ksapanakamarasimghasaitku- 
Vetalablialta-Ghatakarpara-Kalidasah 
Khyato Vaiahamihiro nrpateh sabhayain 
Hatnani vai Vararuci-r-nava Vikramasya, 

occms fir-4 of all in the last chapter of the a.4rul^ical work 

by another KalUasa, who was an 



TIME INDICATIONS IX KIL1DISA 277 

aaliologei whose date cannot but be about 1243 A D. from the 
following considerations : 

In this work in the last chapter the author says that the 
epoch of his work is placed at 3,058 years of Kali elapsed, f.'c., 
34 B.C. -This e'inmfc be the date of the autaor, as it is only 
the date from which the cak'uiathns are started. Hi-: rjle for 
finding the distance of the origin of the Hindu pphor-3 fro n the 
vernal equinox shows that this was zero afc 413 of the S.ila year 
elapsed, or 5'23 A.D. This also cannot be the date of this 
astrologer KfiKda.sa. If we examine his rules for finding when 
the nui and the moon would have numerically equal declinations 
except near about conjunction,* and oppositions, this yields the 
result that at the time of this astrologer, the distance of the 
origin of the Hindu sphere from the vernal eq-iinox was about 
1-3. This muceUrs da'e t aboat 1-243 A.D. This was also the 
finding of the late MM. Sudhakara Dviv^'ii in his Sauskr t 
work named Ganahu Taranyinl, page 46. This author can never 
'be (he same peison as the greatest; Sanskrit poet bearing the 
same name. As-: to the last chapter of this astrological work 
Pandit Dvivedi has paid: 



Ayaiuantiniadhiayo granthakrta jagad-vaficanaya svayaui 
viiaeito \fl, tenaticl itiliasauabbijSena praksipta iti nihsaiii&iyam 
ajanaui&ina} aua-krantifcamjasailhunair granlhasthair vibhati. 

' This last chapter is either wtitten by the author himself 
in order to deceive the world or that it wa-j interpolated by a 
person who was ignorant of history : a conclusion which follows 
as a necessary corollary to the rules given in the body of the 
work for finding the distance of the origin of the Hindu sphere 
from the vernal equinox of date, and for finding the numerical 
equality in declination of the sun and the moon excepting near 
about conjunctions and oppositions.' 

Thus any statement of the Vikramaditya tradition, if found 
only in the last chapter of this astrological work, cannot be taken 
as correct. The King Vikramaditya may be a mere invention, 
The moot point here is to explore earlier and more reliable 



ANCIENT INDIAN CHKONOLOGY 

authors before this tradition may be accepted as true. Sorne 
of the ' nine gems/ however, may have been contemporary. 

Then again the hypothesis that the * Vikrama ' era of having 
been started from 57 or 58 B.C. is also of very questionable 
nature, as its original name was perhaps not 'Vikrama 'era 
but 'Malava* or 'Erta' era. The reader is here referred to 
Chapter XXIV, pages 242-43. 

From the facts stated above we may take it that the old name 
of the eia in question was the Vikrama era. The traditional 
king Vikramaditya of UjjayinI is in ail probability a mythical 
person. He cannot be identified with any of the Gupta emperors 
who assumed the title of Vikramaditya. The now-known 
Samvat eia can also have nothing to do with the time of 
Kalidasa. 

As to the date of Kalidasa, so far as we can reasonably 
deduce from the astronomical data in his works, it comes out 
as about 541-546 A,D., or about the middle of the sixth century 
A.D., and that he is a contemporary of Varahamihira. So far 
as I have seen, the finding in this paper would not go against 
any epigraphic evidence as discovered up to date. 



EPILOGUE 

The book has come to its end but it is felt necessary to make 
some concluding remarks for its future critics in respect of 
certain points. 

First of all, as to Section I treating of the Date of the 
Bharata Battle, it may be put forward that the Mahabharata 
is only a great poem and as such, data derived from it cannot 
form any basis for finding the Date of the Bharata Battle. It may 
also be suggested that the Puranas should more properly be used 
for the purpose. In reply to this it may be said that (1; the 
necessary astronomical data can be found only from the Malia- 
bhdrata and from no other source. (2) In the Garga Samhitd 
(not yet published) there have been found more than one state- 
ment which say or indicate that the Bharata Battle was fought 
at the junction of the Kali and Dvdpara Yugas. Bhattotpala has 
quoted in his commentary on the Brhatsamhitd, XIII, 3 1 a verse 
which runs thus : 



ra ?<cns \\ 

66 At the junction of the Kali and Dvdpara ages, the seven Rsis 
were in the naksatra Maghd ; they, faithful to their austerities, 
were the protectors of the peoples." 

Again in the Garga Sariihita it is also said 2 that the Malid- 
"blidrat a heroes were living at the end of the Dvapara age. This 
"junction" of Kali and Dvapara has been shown in pp. 
35-42, as at January 10, 2454 B.C. The year in this Malia- 
bharata cum Purana KaUynga had the Winter Solstitial reckon- 
ing, in contradistinction to Aryabhata's veinal equinoctial years. 
The date of the Bharata Battle, as determined at 2449 B.C., 
is exactly one luni-solar cycle of five years later than the 
Dvapara-Kali junction year of 2454 B.C. This is a corroboration 

1 Loc cit., page 15. 

3 B- A. B. Bengal, Manuscript, L D. 20 (Forb Will. Coll.), Folio 102, 2. 



28o ANCIENT INDIAN CHRONOLOGY 

of oar finding from the Garga Samhitd, which cannot be only a 
"poem" like the Mahnbhdrata. 

The Puranic evidences as to the Date of the Bharata Battle 
are ail incomplete and faulty as shown in Chapter III. 

The Mdhnbhtirala and the Purdnas belong to the same class 
of literature called Jaya or tales of victory. The following 
exttju-ts from the Miihlblwrala will bear this out: 

(//) 



* # 



f , 1, 61 & 63. 
(i) 



From the first extract we learn that the Mahabharata contains 
the be^innin^a of the Purilnas and Itihdsas (history). In the 
Malribli'lfa'a \ve find that only the Vdyu and Matsya, Purdnas 
ara nipntio^.e.l by name. The second extract says positively that 
the Nith'bhnrata itself is a Jaya or a tale of victory, and it is 
the easiest of this class of literature. The Purdnas are extremely 
faulty in their dynastic lists and tha sum-mrisers who sta f e the 
intevv.il between the birth of Pariksit and the accession of Maha- 
pafluui' Nunda ate hopelessly unreliable. The Muhfibharata as 
a bani^ for fiirling the Date of the Bharata Battle has been shown 
UK fur rupejior to the Pnranas. 

]ji>t of all, it ma ; be nr^ed that BhTs r na ns a hero in Hie great 
fij;ht is an impo-s'bHi^v that hi-i lyinjr on Ili3 bol of arrows for 
58 u'/;lit- before exi^iry in anlic-pat'on of I'-iJ day following Hie 
winter solbtice is a solar myth. The crthoclDX Indian view is 
ranged against this allegation. If we a D r ree ihat this w,is a niyth, 
we should not lose sight o&the fact that the leal necessity for 
creating it lay in correctly finding the begin! ng of the year One 
of the Judhisthira era, of which zero year was the year of the 



EPILOGUE 281 

great battle. Hence even accepting the character of BhTsma 
in th6 fight as a solar myth, the Date of the Bharata Battle as 
found remains valid. In ancient times the first day of the 
year was the day following the winter solstice. Even now Christ's 
birth-day is observed on the 25th December. In the first century 
B.C. the 24th December was the winter solstice day, and 
the 25th December, was the first day of the sun's 
northerly course, or the birth of Christ was synchronous with 
the birth of the year. In both cases the myths may also have 
been created round these great personages on the basis that 
a certain great astronomical event such as the beginning of the 
year coincided with their birth or death. 

In Section II on Ve'dic Antiquity, the heliacal rising of 
different stars in different seasons has been used as a basis for the 
determination of tirr,e. In all these cases the depression of the sun 
below the horizon, at the time of the heliacal rising of stars, has 
been uniformly taken at 18. In the case of the bright stars, 
e.g., Sinus, Regulus, etc., the sun's depression should have been 
taken less than this amount. In this connection we would say 
that we do not know how far accurate were the observers of those 
days of hoary antiquity as to the heliacal risings of stars. We do 
not also know how far the horizon was clear in different seasons 
at Kuruksetra, the assumed centre of Vedic culture, for such 
observations and what was the necessary or accepted altitude of 
the star above the horizon in the several cases. In certain case 
we have admitted possible lowering of the date by a few centuries. 



: n 
f? 1 1 



: u 






n \ 

86U08B 



SOME OPINIONS ON THE RESEAROHES EMBODIED 
IN THE PRESENT WORK 

A 

(-EZ&tract from " Nature, 9 ' January 6, 1940, Vol. 145, No. 8602, 

T 38*89) - 

* c SOME INDIAN ORIC ' T E LIGHT OF ASTKO- 

NOI 3E . 

Among recent cor the Royal Asiatic Society 

of Bengal, several c aetails of a technical character 

ii palaeographical ariu .orical studies bear upon points of 
interest and importance in the archaeological investigation of 
tlae origin a,nd development of Indian civilization. 1 



Conclusions of a more surprising character, based on astro- 
nornical evidence, have been formulated by P. C. Sengupta 
in eu series of papers discussing chronological and other problems 
in early Indian history. The first of these deals with the 
da-te of the Bharata battle, the great conflict which forms 
the centra! incident of that great monument of early Indian 
litei*a.ture, the Mahabharata. The date for this battle, as 
accounted is indicated by three lines of traditional 
at 3102-3101 B.C. The author, on an examination 
of one of these traditions, the evidence of the Yudhishthira era, 

shown that the astronomical references justify the inference 



i J. B Asiatic Boo., Bengal, Let ers 4, 3 (1938), issued September, 1939. 
/ Cii^ ters JI i J&i xm IV an<i v of the present work. 



284 SOME OPINIONS ON BEBEABOHBS 

that the great battle took place in 2449 B.C. He now turns to 
examine the remaining two traditions, the Aryabhata and the 
Puranic traditions. 

The calculation depends upon the dating of the Kaliyuga, 
which the Mahabharata states had just begun and to which the 
date February, 3102 B.C. is assigned. It cannot, however, be 
reconciled with the astronomical Kaliyuga, and is shown to be 
based upon an astronomical calculation in which conditions are 
correct only for A.D. 499, when the Hindu scientific Siddhantas 
came into being. It depends upon an incorrect assumption of the 
position of the solstices of Pandava times and an incorrect annual 
rate of the precession of the equinoxes. A corrected back calcula- 
tion from conditions in the heavens corresponding to those 
recorded in the Mahabharata, that is conditions in the period 
February 1924-35, gives a date January 10, 2454 B.C. as the 
beginning of this Kaliyuga era, and 2449 B.C. as the year of 
the battle. 

This leads to futher inquiry as to observation of the solstices 
in successive ages. This was determined by the phases of the 
moon in the month of Magha, a lunar month of which the 
beginning at the present time may be from January 15 to 
February 11. In the calendar of the Vedic Hindus, this month 
started the five-j ear cycle which began " when the tun, the 
moon and the Dhanisthas (Delphinis) cross the heavens together ; 
it is the beginning of the Yuga, of the month of Magha or Tapas, 
of the light half and of the sun's northerly course." From the 
astronomical conjunctions to which reference is made in the 
Mahabharata, it would appear that this reckoning was started 
(traditionally by Brahma; at about 3050 B.C. 

There are three peculiarities of this month : 

(1) it began with a new-moon - near Delphinis; (2) the 
full-moon was near Eegulus ; (3) the last quarter was conjoined 
with Antares, Such a month did not come every year, but it 
was the standard month of Magha. In our own times, it occurred 
in 1924 during February 5 March 5, a year which for the purpose 
pf this investigation is taken as the gauge year. 



IN ANCIENT INDIAN CHRONOLOGY 285 

References in the Brahmanic and other works directly state 
or indicate the winter solstice of successive Vedic periods. From 
these astronomical references fixing the position of the nicon in 
relation to the winter solstice and the beginning of the month of 
Magha, a matter of ritual importance in connection with the 
year-long and other sacrifices, it has been possible to fix by 
calculation back from the corresponding conditions in recent 
years a series of dates beginning with 3550 B.C , the earliest 
date of the age of the Brahmanas, and covering a period of 1450 
years with a possible error of 400 years. It was thus during this 
period that the Brahmanic literature developed. 

Next is considered Madhu-vidya or the science of Spring, 
which as here interpreted is really the knowledge of the celestial 
signal for the coming of spring, addressed to the Asvins, who are 
identified with a and /B Arietis, the prominent stars in the 
Asvini cluster. The three stars, a, /? and 7 Arietis, form a 
constellation -which is likened to the head of a horse. The 
Asvins are spoken of in several passages of the Rigveda as riding 
in the heavens in their triangular, three-wheeled, and spring- 
bearing chariot . 

From certain references it would seem that when the car of 
the Asvins first becomes visible at dawn, spring began at some 
place in the latitude of Kuruksetra in the Punjab. The jealously 
guarded Madhu-vidya or " science of Spring " was thus nothing 
but knowledge of the celestial signal of the advent of Spring 
the heliacal rising of a, /3 and 7 Arietis. 

By astronomical calculation it can be shown that this event 
at the latitude mentioned took place at, say 4000 B.C. Hence it 
is beyond question that the Vedic Hindus could fiud accurately 
the beginning of winter, spring and all seasons of the year, 

The earliest epigraphic evidence of Vedic chronology from 
cuneiform inscriptions referring to Indra and other gods of the 
horse riding Kharri or Mitanni dates from about 1400 B.C. In 
the absence of further epigraphic evidence, it is pointed out, this 
definite finding of the astronomical evidence derived from the 
literature as to the antiquity and chronology of the Vedas must 



236 SOME OPINIONS ON KESEAKCHES 

be allowed to stand. It establishes, it is maintained, that the 
civilization of the Vedic Hindus was earlier than that of the 
Indus Valley as evidenced by the remaius at Mahenjo-daro t 

Finally, in " When Indra became Maghavan," Mr. Sen- 
gupta turns to the relation of the Vedic god In3ra, the " shedder 
of rain " and " wielder of the thunderbolt/' to the summer 
solstice. The references to this god in the Rigveda, when divested 
of all allegory, suggest that he is the god of the summer solstice, 
while the clouds as represented by a demon are unwilling to 
yield up their watery store until assailed by the thunderbolt 
hurled by the god, 

The monsoons which bring the rains usually burst about June 
22, and there is usually a drought which lasts for about a month 
before the monsoon comes. The demon Susna (drought) is killed 
by Indra. The fight with Vritra or Ahi, the cloud demon, is thus 
an annual affair which takes place when the sun enters the 
summer solstice, Indra withdrawing his raingiving (or annual) 
bow with the coming of autumn. 

When did Indra become the slayer of Vritra? The answer 
given by the Eigveda is when Indra by the rising of Maghas 
became Maghavan. Magbas to us must be the constellation 
Maghas consisting of a, ?;, y, ? /U) and e Leonis, at the heliacal 
rising of which the sun reached the simimer solstice at the latitude 
of Kuruksetra flat. 30 N.) This it is shown must have happened 
in 4170 B.C." 

B 

Sky and Telescope, Vol. I, No. 5., March, 1942. 
Harvard College Observatory, Cambridge, Mass. 
Page 10. News and Notes. 

" ECLIPSE OF JULY 26, 3928 B.C. 1 

Astronomy has come to the aid of the historian in determining 
the time of the earliest known Aryan colonisation in India. 
According to P. C. SeDgupta (Journal of the Eoyal Asiatic Society 

1 C{. Chapter IX of the present work* 



IN ANCIENT INDIAN CHRONOLOGY 287 

of Bengal for August, 1941), this began about 3900 B.C. A solar 
eclipse, described in the Rigveda, had been observed by Atri, one 
of the earliest settlers in the northern Punjab. From various 
historical and etymological considerations, Sengupta deduces that 
the eclipse occurred between the years 4000 and 2400 B.C. He 
then lists five other conations that must be satisfied in the 
determination of the actual date. 

It must have been a central eclipse, taking place on the day 
of the Summer Solstice or the following day. It must have ended 
during the fourth quarter of the day at meridian of Kuruksf tra. 
It was observed from a cave at the foot of a snowcapped- peak, 
either the Himalayas or the Karakoram range. Finally, at the 
place where Atri was, the eclipse did dot reach totality, 

Among the 2*2 central solar eclipses that occurred near the 
Summer Solstice within the given time interval, there is one and 
only one that fulfils all of the required conditions inferred from 
the Rigveda. That one occurred on July 26, 3928 B.C. (Julian^ 
Calendar). . 

Sengupta's painstaking researches thus place the date of the 
first settlement of Aryans in India earlier than previous investi- 
gators believed. To most Americans, whose ancestry can be 
traced but a few hundred years, observations made at so early an 
epoch might appear to have a purely mythological value. It is a 
source of satisfaction to find that they conform with astro- 
nomically predictable facts/' 








ERRATA 




PAOF 


LINK 


FOR 


READ 


8 


Footnote, 1. 5 


wit $9 


^T^tSi 


16 


9 


160X4 


160x3 


17 


27 


120 28' 36" 


102 28' 3G" 


19 


Footnote, 1. 3 


1938 


1939 


24 


'2 


date 


data 


31 


Table noU. 5 and 7 


sagitter 


sagttar 
& 


41 


Footnote, 1. 6 


iatPS^l 


"*IT<TO 


45, 


i- 3 


Epigrapkia 


Epigraphica 


51 


25 


^r%3f 


**& 


64 


Footnote, 1. 4 


^re^T- 


^1 


71 


* * 


' 


W 


71 


1. 2 


i?rfci 


f^zft: 


81 


28 


at 


of 


84 


12 


as have 


as to have 


84 


Footnote, 1. 7 


HTWOT 


HT^nPflf 


85 


I- 2 


W3t 


*JH^t 


88- 


14 


end 


and 


98 


14 


Pcgasi 


Pegasi 


112 


17 


930 


93 


125, 126 


L8 and 17 


1934" (M-hS) 


l96i"=tM-h 


125, 127 


19 and 18 


41" \M-S) 


4r=(M-S) 


145 


Footnote, 1. 2 


in? 


1* 


154 


Sanskrit 


SftfT 


^TflT 


154 





^CHIf 


^TWf 


15H 


Footnote, 1. 14 


heir 


their 


172 


27 


Solstitial 


Solstitial 


204 


Table, 6 


-186 


-885 


210 


8 


T 756 A.D. 


-756 A.D. 


210 


8 


-Ohr. 


T., U hr. 


210 


21 


762 A.D. 


-762 A.D. 


211 


13 


906 A.D. 


-9d6A.L> 


2W 


17 


faltt^WR 


^{^I'^TTTI 



37 1408B 



4300 



1935